The Second shift of the TS EAMCET 2025 Engineering Exam is being conducted on May 3, 2025, between 3:00 P.M. and 6:00 P.M., at multiple centres in Telangana and Andhra Pradesh. Around 75,000 candidates are expected to appear for the same.

The TS EAMCET 2025 Exam will be held in CBT mode and includes 3 important subjects: Mathematics, Physics, and Chemistry. The TS EAMCET Question Paper has a total of 160 multiple-choice questions and is for 160 marks, with 50% of the questions from Mathematics.

The TS EAMCET 2025 May 3rd Shift 2 Question Paper with solution PDF is available here.

TS EAMCET 2025 Question Paper with Solution PDF

TS EAMCET 2025 May 3 Shift 2 Question Paper with Answer Key Download PDF Check Solution
TS EAMCET 2025 May 3 Shift 2 Question Paper (Available) Download Solution with Answer Key


Question 1:

Let \(f: R \rightarrow R\) be defined by \(f(x) = 5^{|x|} + sgn(5^{-x})\), where sgn x denotes signum function of x. Then f is

  • (A) one-one but not onto
  • (B) onto but not one-one
  • (C) both one-one and onto
  • (D) neither one-one nor onto

Question 2:

If the range of the real valued function \(f(x) = \frac{x^2 + x + k}{x^2 - x + k}\) is \([\frac{1}{3}, 3]\), then \(k =\)

  • (A) -2
  • (B) -1
  • (C) 1
  • (D) 2

Question 3:

The value of the greatest integer k satisfying the inequation \(2^{n+4} + 12 \geq k(n+4)\) for all \(n \in N\) is

  • (A) 7
  • (B) 8
  • (C) 9
  • (D) 10

Question 4:

If the system of simultaneous linear equations \(x - 2y + z = 0\), \(2x + 3y + z = 6\) and \(x + 2y + pz = q\) has infinitely many solutions, then

  • (A) \(p + q = 4\)
  • (B) \(pq = 48/49\)
  • (C) \(q - p = 3\)
  • (D) \(p/q = 4/9\)

Question 5:

If the system of linear equations \((\sin\theta)x - y + z = 0\), \(x - (\cos\theta)y + z = 0\), \(x + y + (\sin\theta)z = 0\) has a non-trivial solution, then the least positive value of \(\theta\) is

  • (A) \(\pi/6\)
  • (B) \(\pi/4\)
  • (C) \(\pi/3\)
  • (D) \(\pi/2\)

Question 6:

If \(A = \begin{pmatrix} 1 & 2 & 3
2 & 1 & 1
1 & 3 & 1 \end{pmatrix}\) and \(B = \begin{pmatrix} 2 & 3 & 4
3 & 2 & 2
2 & 4 & 2 \end{pmatrix}\), then \(\sqrt{|Adj(AB)|} =\)

  • (A) 176
  • (B) 208
  • (C) 198
  • (D) 234

Question 7:

If \(A = \begin{pmatrix} 1 & 5 & 2
4 & 1 & 3
2 & 6 & 3 \end{pmatrix}\), then \(|(Adj A)^{-1}| =\)

  • (A) -1
  • (B) 1
  • (C) 4
  • (D) -4

Question 8:

The amplitude of the complex number is:
\[\frac{(\sqrt{3}+i)(1-\sqrt{3}i)}{(-1+i)(-1-i)}\]

  • (A) \(\dfrac{\pi}{2}\)
  • (B) \(\dfrac{\pi}{3}\)
  • (C) \(\dfrac{5\pi}{12}\)
  • (D) \(-\dfrac{\pi}{6}\)

Question 9:

If a complex number \(z = x+iy\) represents a point \(P(x, y)\) in the Argand plane and z satisfies the condition that the imaginary part of \(\frac{z-3}{z+3i}\) is zero, then the locus of the point P is

  • (A) \(x^2+y^2-3x+3y= 0, (x, y) \neq (0,-3)\)
  • (B) \(2xy-3x+3y+9=0, (x, y) \neq (0,-3)\)
  • (C) \(x-y-3=0, (x, y) \neq (0,-3)\)
  • (D) \(x+y+3=0, (x, y) \neq (0,-3)\)

Question 10:

\((\sqrt{3}+i)^{10} + (\sqrt{3}-i)^{10} =\)

  • (A) \(1024\sqrt{3}\)
  • (B) 1024
  • (C) 2048
  • (D) \(512\sqrt{3}\)

Question 11:

Number of real values of \((-1-\sqrt{3}i)^{3/4}\) is

  • (A) 0
  • (B) 1
  • (C) 2
  • (D) 3

Question 12:

If \(\tan\theta\) and \(\cot\theta\) are two distinct roots of the equation \(ax^2+bx+c=0, a\neq0, b\neq0\), then

  • (A) \(\cos 2\theta = -\frac{2b}{c}\)
  • (B) \(\sin 2\theta = -\frac{2c}{b}\)
  • (C) \(\tan 2\theta = \frac{2b}{c}\)
  • (D) \(\cot 2\theta = \frac{2c}{a}\)

Question 13:

Sum of all the roots of the equation \(||2x-3|-4| = 2\) is

  • (A) 8
  • (B) 0
  • (C) 6
  • (D) 9

Question 14:

If the quotient and remainder obtained when the expression \(3x^5-6x^4+2x^3+4x^2-5x+8\) is divided by the expression \(x^2-2x+3\) are \(ax^3+bx^2+cx+d\) and \(px+q\) respectively, then \(ab+cd =\)

  • (A) \(p+2q\)
  • (B) \(p+2q-2\)
  • (C) \(2p+q\)
  • (D) \(2p+q-2\)

Question 15:

If \(\alpha, \beta, \gamma, \delta\) are the roots of the equation \(12x^4-56x^3+89x^2-56x+12=0\) such that \(\alpha\beta = \gamma\delta = 1\) and \(\frac{\alpha+\beta}{\gamma+\delta} > 1\), then \(\frac{\alpha+\beta}{\gamma+\delta} =\)

  • (A) \(65/6\)
  • (B) \(13/2\)
  • (C) \(17/15\)
  • (D) \(15/13\)

Question 16:

If all the letters of the word ACADEMICIAN are permuted in all possible ways then the number of permutations in which no two A's are together and all the consonants are together is

  • (A) 7200
  • (B) 14400
  • (C) 3600
  • (D) 1800

Question 17:

The number of all possible three letter words that can be formed by choosing three letters from the letters of the word FEBRUARY so that a vowel always occupies the middle place is

  • (A) 90
  • (B) 93
  • (C) 126
  • (D) 129

Question 18:

The number of ways in which 6 boys and 4 girls can be arranged in a row such that between any two girls there must be exactly 2 boys is

  • (A) \(6!5!\)
  • (B) \((72)6!\)
  • (C) \((144)5!\)
  • (D) \(4!7!\)

Question 19:

If \(C_0, C_1, C_2, \dots, C_n\) are the binomial coefficients in the expansion of \((1+x)^n\) then the value of \(\sum r^3 \cdot C_r\) when \(n = 5\) is

  • (A) 320
  • (B) 560
  • (C) 720
  • (D) 800

Question 20:

The coefficient of \(x^{12}\) in the expansion of \((x^2+2x+2)^8\) is

  • (A) 1120
  • (B) 2240
  • (C) 2576
  • (D) 4152

Question 21:

If \(\frac{x^2+1}{(x^2+2)(x^2+3)} = \frac{Ax+B}{x^2+2} + \frac{Cx+D}{x^2+3}\), then \(A+B+C+D=\)

  • (A) 0
  • (B) 1
  • (C) -1
  • (D) 6

Question 22:

If \(2 \sin\theta+3 \cos\theta=2\) and \(\theta \neq (2n+1)\frac{\pi}{2}\) then \(\sin\theta+\cos\theta=\)

  • (A) \(5/13\)
  • (B) \(3/5\)
  • (C) \(7/13\)
  • (D) \(4/5\)

Question 23:

If \(\sin A = -\frac{24}{25}\), \(\cos B = \frac{15}{17}\), A does not belong to 4th quadrant and B does not belong to 1st quadrant then \((A + B)\) lies in the quadrant

  • (A) 1st quadrant
  • (B) 2nd quadrant
  • (C) 3rd quadrant
  • (D) 4th quadrant

Question 24:

\(4 \cos\frac{70}{2}\cos\frac{30}{2} - \sin 50 =\)

  • (A) \(\sin 100 + \sin 70 - \sin 30\)
  • (B) \(\sin 100 + \sin 70 - \sin 50\)
  • (C) \(\sin 100 + \sin 70 + \sin 30\)
  • (D) \(\sin 100 + \sin 70 + \sin 50\)

Question 25:

If \(x \in (-\pi,\pi)\) then the number of solutions of the equation \(2 \sin x \sin 3x \sin 5x + \sin 5x \cos 4x = 0\) is

  • (A) 14
  • (B) 12
  • (C) 13
  • (D) 9

Question 26:

The number of values of x satisfying the equation \(Tan^{-1}(x+\frac{\sqrt{2}}{x}) + Tan^{-1}(x-\frac{\sqrt{2}}{x}) = Tan^{-1}(x)\) is

  • (A) 0
  • (B) 1
  • (C) 2
  • (D) 3

Question 27:

\(\coth^2 x - \tanh^2 x =\)

  • (A) \(4cosech2x \tanh 2x\)
  • (B) \(4sech2x \coth 2x\)
  • (C) \(4sech2x \tanh 2x\)
  • (D) \(4\cosh^2 x (cosech2x)^2\)

Question 28:

If \(a=3, b=5, c=7\) are the sides of a triangle ABC, then its circumradius is

  • (A) \(7/\sqrt{3}\)
  • (B) \(15/2\)
  • (C) \(15\sqrt{3}/4\)
  • (D) \(\sqrt{3}/2\)

Question 29:

Two ships leave a port at the same time. One of them moves in the direction of E50\(^\circ\)N with a speed of 8 kmph and the other moves in the direction of S20\(^\circ\)E with a speed of 12 kmph. Then the distance between the ships at the end of 2 hours is (in km)

  • (A) \(8\sqrt{7}\)
  • (B) 34
  • (C) \(8\sqrt{19}\)
  • (D) 32

Question 30:

In a triangle ABC, if \(\vec{BC}=\hat{i}-2\hat{j}+2\hat{k}\) and \(\vec{CA}=6\hat{i}+3\hat{j}-2\hat{k}\), then the perimeter of the triangle is

  • (A) \(5(2+\sqrt{3})\)
  • (B) \(5(2+\sqrt{2})\)
  • (C) \(\sqrt{10}(3+\sqrt{10})\)
  • (D) \(10(2+\sqrt{5})\)

Question 31:

If \(\hat{i}+\hat{j}+\hat{k}\), \(a_1\hat{i}+b_1\hat{j}+c_1\hat{k}\), \(a_2\hat{i}+b_2\hat{j}+c_2\hat{k}\), \(a_3\hat{i}+b_3\hat{j}+c_3\hat{k}\) are the position vectors of the points A, B, C, D respectively, \(\frac{2}{3}(\hat{i}+\hat{j}+\hat{k})\) is the position vector of the centroid of the triangular face BCD of the tetrahedron ABCD, and if \(\alpha\hat{i}+\beta\hat{j}+\gamma\hat{k}\) is the position vector of the centroid of the tetrahedron, then \(2\alpha+\beta+\gamma =\)

  • (A) 3
  • (B) 2
  • (C) \(2/3\)
  • (D) \(3/4\)

Question 32:

If \(\vec{a}=\hat{i}-2\hat{j}+2\hat{k}\) and \(\vec{b}=9\hat{i}+6\hat{j}-18\hat{k}\) are two vectors, then \(\frac{Projection of \vec{b} on \vec{a}}{Projection of \vec{a} on \vec{b}} =\)

  • (A) 21
  • (B) 7
  • (C) \(7/3\)
  • (D) 3

Question 33:

Let \(\vec{a} = \hat{i} +2\hat{j}+3\hat{k}\), \(\vec{b}=2\hat{i}-3\hat{j}+\hat{k}\) and \(\vec{c}=3\hat{i}+\hat{j}-2\hat{k}\) be three vectors. If \(\vec{r}\) is a vector such that \(\vec{r}\cdot\vec{a} = 0\), \(\vec{r}\cdot\vec{b} = -2\) and \(\vec{r}\cdot\vec{c} = 6\) then \(\vec{r}\cdot(3\hat{i}+\hat{j}+\hat{k})= \)

  • (A) 0
  • (B) 1
  • (C) 2
  • (D) 3

Question 34:

Let \(\vec{a}=\hat{i}-\hat{j}+\hat{k}\), \(\vec{b}=\hat{i}-2\hat{j}-2\hat{k}\), \(\vec{c}=6\hat{i}+3\hat{j}-2\hat{k}\) be three vectors. If \(\vec{d}\) is a vector perpendicular to both \(\vec{a}\), \(\vec{b}\) and \(|\vec{d}\times\vec{c}|=14\), then \(|\vec{d}\cdot\vec{c}|=\)

  • (A) 35
  • (B) 70
  • (C) 140
  • (D) 105

Question 35:

The mean deviation from the mean of the discrete data 2, 3, 5, 7, 11, 13, 17, 19, 22 is

  • (A) 8
  • (B) 7.5
  • (C) 5.5
  • (D) 6

Question 36:

Out of the given 25 consecutive positive integers, three integers are drawn. If the least integer among given 25 integers is an odd number, then the probability that the sum of the three integers drawn is an even number is

  • (A) \(289/575\)
  • (B) \(286/575\)
  • (C) \(288/575\)
  • (D) \(287/575\)

Question 37:

If three dice are thrown at a time, then the probability of getting the sum of the numbers on them as a prime number is

  • (A) \(3/8\)
  • (B) \(73/216\)
  • (C) \(4/27\)
  • (D) \(5/54\)

Question 38:

Three companies C1, C2, C3 produce car tyres. A car manufacturing company buys 40% of its requirement from C1, 35% from C2 and 25% from C3. The company knows that 2% of the tyres supplied by C1, 3% by C2 and 4% by C3 are defective. If a tyre chosen at random from the consignment received is found defective then the probability that it was supplied by C2 is

  • (A) \(7/19\)
  • (B) \(12/19\)
  • (C) \(10/57\)
  • (D) \(26/57\)

Question 39:

The probability distribution of a random variable X is given below. Then, the standard deviation of X is.


  • (A) 5
  • (B) 11
  • (C) \(\sqrt{11}\)
  • (D) \(\sqrt{5}\)

Question 40:

If the mean and variance of a binomial distribution are \(\frac{4}{3}\) and \(\frac{10}{9}\) respectively, then \(P(X \geq 6) =\)

  • (A) \(41/6^8\)
  • (B) \(741/6^8\)
  • (C) \(1-741/6^8\)
  • (D) \(1-41/6^8\)

Question 41:

A straight line passing through a point (3,2) cuts X and Y-axes at the points A and B respectively. If a point P divides AB in the ratio 2:3, then the equation of the locus of point P is

  • (A) \(\frac{9}{x}+\frac{4}{y}=1\)
  • (B) \(9x+4y=5xy\)
  • (C) \(4x+9y=5xy\)
  • (D) \(\frac{4}{x}+\frac{9}{y}=1\)

Question 42:

By shifting the origin to the point (-1,2) through translation of axes, if \(ax^2+2hxy+by^2+2gx+2fy+c=0\) is the transformed equation of \(2x'^2-x'y'+y'^2-3x'+4y'-5=0\), then \(2(f+g+h) =\)

  • (A) \(a+b+c\)
  • (B) \(a-5(b+c)\)
  • (C) \(3(a+b+c)\)
  • (D) \(c-5(a+b)\)

Question 43:

If a line L passing through the point A(-2,4) makes an angle of 60\(^\circ\) with the positive direction of X-axis in anti-clockwise direction and B(p,q) lying in the 3\(^rd\) quadrant is a point on L at the distance of 6 units from the point A, then \(\sqrt{p^2+q^2-8q} =\)

  • (A) 6
  • (B) 7
  • (C) 8
  • (D) 9

Question 44:

If the perpendicular drawn from the point (2,-3) to the straight line \(4x-3y+8=0\) meets it at M(a,b) and \(a^3-b^3=k^3\), then \(k =\)

  • (A) 1
  • (B) -1
  • (C) 2
  • (D) -2

Question 45:

Let Q be the image of a point P(1,2) with respect to the line \(x+y+1=0\) and R be the image of Q with respect to the line \(x-y-1=0\). If M and N are the midpoints of PQ and QR respectively, then MN =

  • (A) \(\sqrt{10}\)
  • (B) 4
  • (C) \(\sqrt{22}\)
  • (D) 5

Question 46:

If the slopes of the lines represented by the equation \(6x^2+2hxy+4y^2 = 0\) are in the ratio 2:3, then the value of h such that both the lines make acute angles with the positive X-axis measured in positive direction is

  • (A) 5
  • (B) \(5/2\)
  • (C) -5
  • (D) \(-5/2\)

Question 47:

If (3,-2) is the centre of the circle \(S= x^2+y^2+2gx+2fy-23=0\) and A is a point on the circle S = 0 such that its distance from a point P(-1,-5) is least, then A =

  • (A) \((3,-2)\)
  • (B) \((9/5, 28/5)\)
  • (C) \((3/5, 2/5)\)
  • (D) \((-9/5, -28/5)\)

Question 48:

Two circles which touch both the coordinate axes intersect at the points A and B. If A = (1,2), then AB =

  • (A) 5
  • (B) 13
  • (C) \(2\sqrt{2}\)
  • (D) \(\sqrt{2}\)

Question 49:

The line \(4x-3y+2 = 0\) intersects the circle \(x^2+y^2-2x+6y+c=0\) at two points A, B and AB=8. If (1,k) is a point on the given circle and \(k > 0\), then \(k =\)

  • (A) 8
  • (B) 4
  • (C) 2
  • (D) 1

Question 50:

If \(2x-3y+5=0\) and \(4x-5y+7=0\) are the equations of the normals drawn to a circle and (2,5) is a point on the given circle, then the radius of the circle is

  • (A) 1
  • (B) 2
  • (C) 3
  • (D) 4

Question 51:

If \((\alpha,\beta)\) is the centre of the circle which passes through the point (1,-1) and cuts the circles \(x^2 + y^2+2x-3y-5=0\), \(x^2+y^2-3x+2y+1=0\) orthogonally, then \(\alpha-5\beta =\)

  • (A) -10
  • (B) 5
  • (C) -11
  • (D) 10

Question 52:

The centre of the circle touching the circles \(x^2+y^2-4x-6y-12=0\), \(x^2+y^2+6x+18y+26=0\) at their point of contact and passing through the point (1,-1) is

  • (A) \((1/3, -1)\)
  • (B) \((1/5, 6/5)\)
  • (C) \((1/2, 1/2)\)
  • (D) \((-1/4, -1/2)\)

Question 53:

The number of normals that can be drawn through the point (2,0) to the parabola \(y^2 = 7x\) is

  • (A) 0
  • (B) 1
  • (C) 2
  • (D) 3

Question 54:

If \(m_1\) and \(m_2\) are the slopes of the tangents drawn from the point (1,4) to the parabola \(y^2 = 11x\) then \(2(m_1^2 + m_2^2) =\)

  • (A) 24
  • (B) 22
  • (C) 21
  • (D) 18

Question 55:

If the perpendicular distance from the focus of an ellipse \(\frac{x^2}{9} + \frac{y^2}{b^2} = 1\) (\(b<3\)) to its corresponding directrix is \(\frac{4}{\sqrt{5}}\), then the slope of the tangent to this ellipse drawn at \((\frac{3}{\sqrt{2}}, \frac{b}{\sqrt{2}})\) is

  • (A) \(-2/3\)
  • (B) \(2/3\)
  • (C) \(-3/2\)
  • (D) \(3/2\)

Question 56:

The length of the chord of the ellipse \(\frac{x^2}{4} + y^2 = 1\) formed on the line \(y = x+1\) is

  • (A) \(2\sqrt{2}\)
  • (B) \(4\sqrt{2}/5\)
  • (C) \(4\sqrt{2}\)
  • (D) \(8\sqrt{2}/5\)

Question 57:

Let P, Q, R, S be the points of intersection of the circle \(x^2 + y^2 = 4\) and the hyperbola \(xy = \sqrt{3}\). If P = \((\alpha,\beta)\) and \(\alpha > \beta > 0\), then the equation of the tangent drawn at P to the hyperbola is

  • (A) \(x+y=2\)
  • (B) \(x+\sqrt{3}y=2\sqrt{3}\)
  • (C) \(\sqrt{3}x+y=\sqrt{3}\)
  • (D) \(x-y=0\)

Question 58:

The number of values of 'k' for which the points (-4,9,k), (-1,6,k), (0,7,10) form a right-angled isosceles triangle is

  • (A) 0
  • (B) 1
  • (C) 2
  • (D) 4

Question 59:

A line makes angles 60\(^\circ\), 45\(^\circ\), \(\theta\) with positive X, Y, Z-axes respectively. If \(\theta\) is an acute angle, then \(\tan\theta =\)

  • (A) \(\sqrt{3}\)
  • (B) \(1/\sqrt{3}\)
  • (C) 1
  • (D) 2

Question 60:

If the foot of the perpendicular drawn from the point (2,0,-3) to the plane \(\pi\) is (1,-2,0) and the equation of the plane is \(ax+by-3z+d=0\) then \(a+b+d=\)

  • (A) 0
  • (B) 1
  • (C) 6
  • (D) 2

Question 61:

If \([t]\) represents the greatest integer \(\leq t\) then the value of \(\lim_{x\to 3} \frac{11-[2-x]}{[x+10]}\) is

  • (A) 1
  • (B) 8
  • (C) 5
  • (D) does not exist

Question 62:

If the real valued function \(f(x) = \begin{cases} \frac{\cos 3x-\cos x}{x \sin x} & if x < 0
p & if x=0
\frac{\log(1+q \sin x)}{x} & if x > 0 \end{cases}\) is continuous at \(x=0\) then \(p+q=\)

  • (A) 4
  • (B) -4
  • (C) 8
  • (D) -8

Question 63:

If \(y = \sqrt{\log(x^2+1)+\sqrt{\log(x^2+1)+\sqrt{\log(x^2+1)+...}}}\), \(|x|<1\), then \(\frac{dy}{dx} =\)

  • (A) \(\frac{x^2+1}{2y-1}\)
  • (B) \(\frac{2x}{2y-1}\)
  • (C) \(\frac{1}{(x^2+1)(2y-1)}\)
  • (D) \(\frac{2x}{(x^2+1)(2y-1)}\)

Question 64:

If \(x = \sqrt{1-\tan y}\), then \(\frac{dy}{dx} =\)

  • (A) \(\frac{2x}{x^4+2x^2+2}\)
  • (B) \(-\frac{2x}{x^4-2x^2+2}\)
  • (C) \(\frac{2x}{x^4-2x^2+2}\)
  • (D) \(-\frac{2x}{x^4+2x^2+2}\)

Question 65:

If \(y = Sec^{-1}x\), then \(\frac{d^2y}{dx^2} =\)

  • (A) \(\frac{1-2x^2}{x|x|(x^2-1)^{3/2}}\)
  • (B) \(\frac{1-x^2}{x^2(x^2-1)^{3/2}}\)
  • (C) \(-\frac{1-x^2}{x^2(x^2-1)^{3/2}}\)
  • (D) \(\frac{1+2x^2}{x|x|(x^2-1)^{3/2}}\)

Question 66:

If \(x = \sin 2\theta \cos 3\theta\), \(y = \sin 3\theta \cos 2\theta\), then \(\frac{dy}{dx} =\)

  • (A) \(\frac{2 \cos 5\theta+\sin 3\theta \sin 2\theta}{2 \cos 5\theta-\cos 3\theta \cos 2\theta}\)
  • (B) \(\frac{2 \cos 5\theta-\sin 3\theta \sin 2\theta}{2 \cos 5\theta+\cos 3\theta \cos 2\theta}\)
  • (C) \(\frac{2 \cos 5\theta+\cos 3\theta \cos 2\theta}{2 \cos 5\theta-\sin 3\theta \sin 2\theta}\)
  • (D) \(\frac{2 \cos 5\theta-\sin 3\theta \sin 2\theta}{2 \cos 5\theta-\cos 3\theta \cos 2\theta}\)

Question 67:

If the tangent and the normal drawn to the curve \(xy^2 + x^2y = 12\) at the point (1,3) meet the X-axis in T and N respectively, then TN =

  • (A) \(7/5\)
  • (B) \(45/7\)
  • (C) \(3\sqrt{274}/7\)
  • (D) \(274/35\)

Question 68:

A man of 5 feet height is walking away from a light fixed at a height of 15 feet at the rate of K miles/hour. If the rate of increase of his shadow is \(\frac{11}{5}\) feet/sec, then K = (Take 1 mile = 5280 feet)

  • (A) 2
  • (B) 3
  • (C) 4
  • (D) 5

Question 69:

There is a possible error of 0.03 cm in a scale of length 1 foot with which the height of a closed right circular cylinder and the diameter of a sphere are measured as 3.5 feet each. If the radii of both cylinder and sphere are same, then the approximate error in the sum of the surface areas of both cylinder and sphere is (in square feet)

  • (A) 0.385
  • (B) 0.0962
  • (C) 0.77
  • (D) 0.1925

Question 70:

For a real number 'a', if a real valued function \(f(x) = 4x^3 + ax^2 + 3x - 2\) is monotonic in its domain, then the range of 'a' is

  • (A) (-6,6)
  • (B) Empty set
  • (C) (-2,2)
  • (D) (2,4)

Question 71:

If the point P(\(x_1, y_1\)) lying on the curve \(y = x^2-x+1\) is the closest point to the line \(y = x-3\) then the perpendicular distance from P to the line \(3x+4y-2=0\) is

  • (A) \(16/5\)
  • (B) 4
  • (C) 1
  • (D) \(7/5\)

Question 72:

\(\int \frac{3^x(x\log 3 - 1)}{x^2} dx =\)

  • (A) \(x \cdot 3^x + c\)
  • (B) \(\frac{3^x}{x^2} + c\)
  • (C) \(x^2 3^x + c\)
  • (D) \(\frac{3^x}{x} + c\)

Question 73:

If \(\frac{5\pi}{4} < x < \frac{7\pi}{4}\), then \(\int \sqrt{\frac{1-\sin 2x}{1+\sin 2x}} dx =\)

  • (A) \(-\sec^2(\frac{\pi}{4}-x)+c\)
  • (B) \(-\log\sec(\frac{\pi}{4}-x)+c\)
  • (C) \(\sec^2(\frac{\pi}{4}-x)+c\)
  • (D) \(\log\sec(\frac{\pi}{4}-x)+c\)

Question 74:

\(\int xTan^{-1}\sqrt{\frac{1+x^2}{1-x^2}}dx=\)

  • (A) \(\frac{x^2}{4}(\pi-Cos^{-1}x^2)+\frac{1}{4}\sqrt{1-x^4}+c\)
  • (B) \(\frac{x^2}{4}(\pi-Cos^{-1}x^2)-\frac{1}{4}\sqrt{1-x^4}+c\)
  • (C) \(\frac{x^2}{4}(\pi+Cos^{-1}x^2)-\frac{1}{4}\sqrt{1-x^4}+c\)
  • (D) \(\frac{x^2}{4}(\pi+Cos^{-1}x^2)-\frac{1}{4}\sqrt{1-x^2}+c\)

Question 75:

\(\int \frac{1}{(2\cos x + \sin x)^2} dx =\)

  • (A) \(\frac{1}{2+\tan x} + c\)
  • (B) \(-\frac{1}{2\tan x+1} + c\)
  • (C) \(\frac{\cos x}{\cos x+2\sin x} + c\)
  • (D) \(\frac{\cos x}{2\cos x + \sin x} + c\)

Question 76:

\(\int_{-1}^{1} \frac{\log 2 - \log(1+x)}{\sqrt{1-x^2}} dx =\)

  • (A) \(\frac{\pi}{8}\log 2\)
  • (B) \(\frac{\pi}{2}\log 2\)
  • (C) \(\frac{\pi}{4}\log 2\)
  • (D) \(2\pi\log 2\)

Question 77:

\(\int_{0}^{\pi/4} \frac{\sec x}{3\cos x + 4\sin x} dx =\)

  • (A) \(\log(7/3)\)
  • (B) \(\frac{1}{4}\log(7/3)\)
  • (C) \(\frac{1}{4}\log 7\)
  • (D) \(\log 7\)

Question 78:

\(\int_{-2}^{4} |2-x^2| dx =\)

  • (A) \(\frac{8\sqrt{2}-3}{3}\)
  • (B) \(\frac{16\sqrt{2}}{3}+12\)
  • (C) \(\frac{16\sqrt{2}-3}{3}\)
  • (D) \(\frac{8\sqrt{2}+12}{3}\)

Question 79:

The general solution of the differential equation \(\frac{dy}{dx} + (\sec x \csc x)y = \cos^2 x\) is

  • (A) \(y \sec^2 x = \sin^2 x + c\)
  • (B) \(y \sec^2 x = \tan x + c\)
  • (C) \(y \tan x = \sin x \cos x + c\)
  • (D) \(2y \tan x = \sin^2 x + c\)

Question 80:

If the differential equation having \(y = Ae^x + B\sin x\) as its general solution is \(f(x)\frac{d^2y}{dx^2}+g(x)\frac{dy}{dx}+h(x)y=0\), then \(f(x)+g(x)+h(x) =\)

  • (A) \(2\cos x\)
  • (B) \(4\sin x\)
  • (C) 0
  • (D) \(\cos x - \sin x\)

Question 81:

The range of weak nuclear force is of the order of

  • (A) \(10^{16}\) m
  • (B) \(10^{-10}\) m
  • (C) \(10^{10}\) m
  • (D) \(10^{-16}\) m

Question 82:

A piece of length 3.532 m is cut from a rod of length 43.4 m. The length of the remaining rod in metre is (up to correct significant figures)

  • (A) 39.9
  • (B) 39.8
  • (C) 39.868
  • (D) 39.87

Question 83:

A person wearing a parachute jumps off a plane from a height of 2 km from the ground and falls freely for 20 m before his parachute opens. After his parachute opens if he continues to move uniformly with the velocity attained due to his freefall, the total time taken by the person to reach the ground is (Acceleration due to gravity = 10 ms\(^{-2}\))

  • (A) 99 s
  • (B) 100 s
  • (C) 101 s
  • (D) 102 s

Question 84:

A ball projected at an angle of 45\(^\circ\) with the horizontal crosses two points at equal heights separated by a distance at times 2 s and 8 s respectively. The horizontal distance between the two points is (Acceleration due to gravity = 10 ms\(^{-2}\))

  • (A) 300 m
  • (B) 400 m
  • (C) 500 m
  • (D) 600 m

Question 85:

A truck of mass 8 ton is carrying a block of mass 2 ton. If a breaking force of 25 kN is applied on the truck, then the frictional force acting on the block is (Coefficient of static friction between the block and the truck is 0.3)

  • (A) 6250 N
  • (B) 6000 N
  • (C) 5000 N
  • (D) 1000 N

Question 86:

The work done in displacing a particle from \(y=a\) to \(y = 2a\) by a force \(F = -\frac{K}{y^2}\) acting along y-axis is

  • (A) \(5K/8a\)
  • (B) \(14K/8a^3\)
  • (C) \(-K/a^2\)
  • (D) \(-K/2a\)

Question 87:

Due to the presence of air resistance, if a body dropped from a height of 20 m reaches the ground with a speed of 18ms\(^{-1}\), then the time taken by the body to reach the ground is nearly

  • (A) 1.8 s
  • (B) 2.2 s
  • (C) 2 s
  • (D) 2.5 s

Question 88:

A balance is made using a uniform metre scale of mass 100 g and two plates each of mass 200 g fixed at the two ends of the scale and the balance is pivoted at 45 cm mark of the scale. The error when 300 g weight is placed in the plate at 0 cm to weigh vegetables placed in the plate at 100 cm is

  • (A) 36.4 g
  • (B) 63.6 g
  • (C) 200 g
  • (D) 100 g

Question 89:

The ratio of radii of gyration of a thin circular ring and a circular disc of same radius about a tangential axis in their own planes is \(\sqrt{12}:\sqrt{K}\). The value of K is

  • (A) 10
  • (B) 24
  • (C) 5
  • (D) 12

Question 90:

At a given place, to increase the number of oscillations made by a simple pendulum in one minute from 72 to 90, the length of the pendulum is to be decreased by

  • (A) 64%
  • (B) 36%
  • (C) 50%
  • (D) 56%

Question 91:

If the orbital speed of a body revolving in a circular path near the surface of the earth is 8 kms\(^{-1}\), then the orbital speed of a body revolving around the earth in a circular orbit at height of 19,200 km from the surface of earth is (Radius of the earth = 6400 km)

  • (A) 4 kms\(^{-1}\)
  • (B) 6 kms\(^{-1}\)
  • (C) 7.5 kms\(^{-1}\)
  • (D) 9 kms\(^{-1}\)

Question 92:

The Young's modulus and Poisson's ratio of a material are respectively Y and \(\sigma\). The force required to decrease the area of cross-section of a wire made of this material by \(\Delta A\) is

  • (A) \(\frac{Y\Delta A}{4\sigma}\)
  • (B) \(\frac{2Y\Delta A}{\sigma}\)
  • (C) \(\frac{Y\Delta A}{2\sigma}\)
  • (D) \(\frac{Y\Delta A}{\sigma}\)

Question 93:

A thin film of water is formed between two straight parallel wires each of length 8 cm separated by distance of 0.6 cm. The work done to increase the distance between the wires to 0.8 cm is (Surface tension of water = 0.07 Nm\(^{-1}\))

  • (A) 33.6 \(\mu\)J
  • (B) 22.4 \(\mu\)J
  • (C) 11.2 \(\mu\)J
  • (D) 44.8 \(\mu\)J

Question 94:

A rain drop of diameter 1 mm falls with a terminal velocity of 0.7 ms\(^{-1}\) in air. If the coefficient of viscosity of air is \(2\times10^{-5}\) Pas, the viscous force on the rain drop is

  • (A) \(13.2\times10^{-8}\) N
  • (B) \(6.6\times10^{-8}\) N
  • (C) \(26.4\times10^{-8}\) N
  • (D) \(10.4\times10^{-8}\) N

Question 95:

The temperature at which the reading on Fahrenheit scale becomes 90% more than the reading on Celsius scale is

  • (A) 280 \(^\circ\)F
  • (B) 580 \(^\circ\)F
  • (C) 608 \(^\circ\)F
  • (D) 320 \(^\circ\)F

Question 96:

A rectangular ice box of total surface area of 1000 cm\(^2\) initially contains 1.5 kg of ice at 0 \(^\circ\)C. If the thickness of the walls of the box is 2 mm and the temperature outside the box is 42 \(^\circ\)C, then the mass of the ice remaining in the box after 160 minutes is (Thermal conductivity of the material of the box = \(10^{-2}\) Wm\(^{-1}\)K\(^{-1}\) and latent heat of the fusion of ice = \(336\times10^3\) Jkg\(^{-1}\))

  • (A) 0.6 kg
  • (B) 0.9 kg
  • (C) 0.8 kg
  • (D) 0.7 kg

Question 97:

At constant pressure, equal amounts of heat are supplied to a monatomic gas and a diatomic gas separately. The ratio of the increases in internal energies of the two gases is

  • (A) 1:1
  • (B) 9:49
  • (C) 3:7
  • (D) 21:25

Question 98:

If the rms speed of the molecules of a gas at a temperature of 77 \(^\circ\)C is 50 ms\(^{-1}\), then the rms speed of the same gas molecules at a temperature of 150.5 \(^\circ\)C is

  • (A) 65 ms\(^{-1}\)
  • (B) 35 ms\(^{-1}\)
  • (C) 55 ms\(^{-1}\)
  • (D) 45 ms\(^{-1}\)

Question 99:

Two tuning forks of frequencies 320 Hz and 323 Hz are vibrated together. The time interval between a maximum sound and its adjacent minimum sound heard by an observer is

  • (A) 1/6 s
  • (B) 1/3 s
  • (C) 1/12 s
  • (D) 1/9 s

Question 100:

The frequency of sound heard by an observer moving towards a stationary source with certain speed is \(n_1\) and if the observer moves away from the same source with same speed, the frequency of sound heard by the observer is \(n_2\). If the speed of sound in air is 340ms\(^{-1}\) and \(n_1 : n_2 = 71:65\), then speed of observer is

  • (A) 36 kmph
  • (B) 27 kmph
  • (C) 15 kmph
  • (D) 54 kmph

Question 101:

A Cassegrain telescope uses two mirrors of radii of curvature 25 cm and 16 cm separated by a distance of 2.5 cm. The position of the final image of an object at infinity is

  • (A) 40 cm from convex mirror
  • (B) 4.44 cm from concave mirror
  • (C) 4.44 cm from convex mirror
  • (D) 40 cm from concave mirror

Question 102:

A convex lens of radii of curvature 6 cm and 12 cm is immersed in a liquid of refractive index 1.3. If the refractive index of the material of the lens is 1.5, then the focal length of the lens when immersed in the liquid is

  • (A) 39 cm
  • (B) 13 cm
  • (C) 26 cm
  • (D) 52 cm

Question 103:

When unpolarised light from air incidents on the surface of a medium of refractive index \(\sqrt{3}\), then the reflected light is totally polarised. The angle of refraction is

  • (A) 30\(^\circ\)
  • (B) 53\(^\circ\)
  • (C) 60\(^\circ\)
  • (D) 37\(^\circ\)

Question 104:

An alpha particle and a proton are accelerated from rest in a uniform electric field. The ratio of the times taken by proton and alpha particle to attain equal displacements is

  • (A) \(\sqrt{2}:1\)
  • (B) \(1:2\)
  • (C) \(1:\sqrt{2}\)
  • (D) \(2:1\)

Question 105:

A parallel plate capacitor with air as dielectric has a capacitance of 4 \(\mu\)F. The space between the plates of the capacitor is completely filled with a material of dielectric constant 5 and charged to a potential of 100 V. The work done to completely remove the dielectric material after the capacitor is disconnected from the battery is

  • (A) 0.1 J
  • (B) 0.5 J
  • (C) 0.6 J
  • (D) 0.4 J

Question 106:

The potential difference between the terminals of a cell is 20 V when a current of 2 A flows through the circuit. When the direction of current in the circuit is reversed, the potential difference between the terminals of the cell is 30 V. The internal resistance of the cell is

  • (A) 1 \(\Omega\)
  • (B) 1.5 \(\Omega\)
  • (C) 2 \(\Omega\)
  • (D) 2.5 \(\Omega\)

Question 107:

A straight uniform wire of resistance 36 \(\Omega\) is bent in the form of a semi-circular loop. The effective resistance between the ends of the diameter of the semi-circular loop is

  • (A) \(56/9 \Omega\)
  • (B) \(36/7 \Omega\)
  • (C) \(99/7 \Omega\)
  • (D) \(77/9 \Omega\)

Question 108:

An alpha particle moving with certain speed towards east enters a uniform magnetic field directed vertically up. The alpha particle will then move in

  • (A) vertical circular path with the same speed
  • (B) horizontal circular path with the same speed
  • (C) vertical circular path with increased speed
  • (D) vertical circular path with decreased speed

Question 109:

The ratios of the voltage sensitivities, resistances and areas of the coils of two moving coil galvanometers A and B are 4:3, 3:4 and 1:2 respectively. If the number of turns of the coil of galvanometer A is 200, then the number of turns of the coil of galvanometer B is (All other quantities remain same in both the cases)

  • (A) 100
  • (B) 150
  • (C) 200
  • (D) 400

Question 110:

A solenoid of 1000 turns per metre has a core of material with relative permeability 400. The windings of the solenoid are insulated from the core and a current of 2 A is passed through the solenoid. Then the value of the magnetic intensity inside the solenoid is

  • (A) \(2\times10^3\) Am\(^{-1}\)
  • (B) 1.0 Am\(^{-1}\)
  • (C) \(8\times10^5\) Am\(^{-1}\)
  • (D) 794 Am\(^{-1}\)

Question 111:

An emf of 2.8 mV is induced in a rectangular loop of area 150 cm\(^2\) when the current in the loop changes from 3 A to 8 A in a time of 0.2 s. Then the self-inductance of the loop is

  • (A) 112 \(\mu\)H
  • (B) 56 \(\mu\)H
  • (C) 28 \(\mu\)H
  • (D) 84 \(\mu\)H

Question 112:

A capacitor and a resistor of resistance \(100\sqrt{3}\Omega\) are connected in series to an ac source of voltage \(100\sin(200t)\) V, where 't' is time in second. If the phase difference between the voltage and the current in the circuit is 30\(^\circ\), then the capacitance of the capacitor is

  • (A) 30 \(\mu\)F
  • (B) 50 \(\mu\)F
  • (C) 100 \(\mu\)F
  • (D) 150 \(\mu\)F

Question 113:

The amplitude of the electric field associated with a light beam of intensity \(\frac{15}{\pi}\) Wm\(^{-2}\) is

  • (A) 120 NC\(^{-1}\)
  • (B) 15 NC\(^{-1}\)
  • (C) 60 NC\(^{-1}\)
  • (D) 30 NC\(^{-1}\)

Question 114:

When photons incident on a photosensitive material of work function 1.5 eV, the maximum velocity of the emitted photoelectrons is \(8\times10^5\) ms\(^{-1}\). The stopping potential of the photoelectrons is (Mass of the electron \(= 9\times10^{-31}\) kg and charge of the electron \(= 1.6\times10^{-19}\) C)

  • (A) 1.8 V
  • (B) 1.5 V
  • (C) 2.1 V
  • (D) 2.4 V

Question 115:

The potential energy of an electron in an orbit of hydrogen atom is -6.8 eV. The de Broglie wavelength of the electron in this orbit is (\(r_0\) is Bohr radius)

  • (A) \(2\pi r_0\)
  • (B) \(4\pi r_0\)
  • (C) \(\pi r_0\)
  • (D) \(3\pi r_0\)

Question 116:

If a radioactive substance decays 10% in every 16 hours, then the percentage of the radioactive substance that remains after 2 days is

  • (A) 82.2
  • (B) 18.8
  • (C) 27.1
  • (D) 72.9

Question 117:

If a nucleus P converts into a nucleus Q by the decay of one alpha particle and two \(\beta^-\) particles, then the nuclei P and Q are

  • (A) Isotopes
  • (B) Isobars
  • (C) Isotones
  • (D) Isomers

Question 118:

The graph between the input voltage (\(V_i\)) and the output voltage (\(V_o\)) of a transistor connected in common emitter configuration is shown in the figure. The active, saturation and cutoff regions of the transistor are respectively


  • (A) I, II and III
  • (B) II, III and I
  • (C) II, I and III
  • (D) I, III and II

Question 119:

Which of the following logic gates is a universal gate?

  • (A) AND
  • (B) OR
  • (C) NOT
  • (D) NAND

Question 120:

The layer of the atmosphere which efficiently reflects high frequency waves particularly at night is

  • (A) Troposphere
  • (B) Stratosphere
  • (C) Mesosphere
  • (D) Thermosphere

Question 121:

In the atomic spectrum of hydrogen, the wavelengths of the spectral lines corresponding to electronic transitions (i) n = 4 to n = 2 and (ii) n = 3 to n = 1 are \(\lambda_1\) and \(\lambda_2\) \AA{ respectively. The value of \((\lambda_1 - \lambda_2)\) (in cm) is (\(R_H\) = Rydberg constant)

  • (A) \(\frac{1}{R_H}\left[\frac{24}{101}\right]\)
  • (B) \(R_H\left[\frac{24}{101}\right]\)
  • (C) \(\frac{1}{R_H}\left[\frac{101}{24}\right]\)
  • (D) \(R_H\left[\frac{101}{24}\right]\)

Question 122:

Work functions of four metals M\(_1\), M\(_2\), M\(_3\) and M\(_4\) are 4.8, 4.3, 4.75 and 3.75 eV respectively. The metals which do not show photoelectric effect when light of wavelength 310 nm falls on the metals are

  • (A) M\(_1\), M\(_2\) only
  • (B) M\(_1\), M\(_3\) only
  • (C) M\(_1\), M\(_2\), M\(_3\) only
  • (D) M\(_1\), M\(_2\), M\(_4\) only

Question 123:

In second period of the modern periodic table, two elements X and Y have higher first ionization enthalpy values than the preceding and succeeding elements. X and Y are respectively

  • (A) B, C
  • (B) Al, S
  • (C) Be, N
  • (D) Na, S

Question 124:

Consider the following pairs of elements and identify the pairs of elements which have nearly same atomic radius.
I. Y, La
II. Zr, Hf
III. Mo, W
IV. Cr, Mo

  • (A) I \& II
  • (B) II \& III
  • (C) III \& IV
  • (D) I \& III

Question 125:

If the sum of bond orders of O\(_2\) and O\(_2^-\) is x, then bond order of O\(_2^+\) will be

  • (A) 1.20x
  • (B) 1.33x
  • (C) 1.50x
  • (D) 2.50x

Question 126:

Identify the molecule / ion in which the ratio of \(\sigma\) to \(\pi\) bonds is 3:2

  • (A) HCO\(_3^-\)
  • (B) CH\(_2\)(CN)\(_2\)
  • (C) HClO\(_4\)
  • (D) XeO\(_3\)

Question 127:

At 298K, a flask 'A' of unknown volume (V) contains oxygen at 5 atm. Another flask 'B' of volume 2L contains helium at 3 atm. Two flasks are connected together by a small tube of zero volume. After the two gases are completely mixed, if the resulting mixture is found to have the mole fraction of oxygen as 0.2, the volume of flask 'A' (in L) is (Assume oxygen and helium as ideal gases)

  • (A) 0.1
  • (B) 0.3
  • (C) 0.2
  • (D) 0.4

Question 128:

In which of the following, oxidation state of nitrogen is lowest?

  • (A) NH\(_2\)OH
  • (B) NH\(_4\)Cl
  • (C) N\(_2\)H\(_4\)
  • (D) HNO\(_2\)

Question 129:

Which of the following processes are reversible?
I. Vaporization of a liquid at its boiling point.
II. Expansion of gas into vacuum.
III. Transformation of a solid substance into liquid at its melting point.
IV. Neutralization of an acid by a base.

  • (A) I \& III
  • (B) II \& III
  • (C) II \& IV
  • (D) I \& IV

Question 130:

At T(K) in a saturated solution of MgCO\(_3\) and Ag\(_2\)CO\(_3\), if the concentration of Mg\(^{2+}\) ion is \(3.2\times10^{-5}\) M, then the concentration of Ag\(^+\) ion in the solution will be [Given: \(K_{sp}(MgCO_3)=1.6\times10^{-6}\) and \(K_{sp}(Ag_2CO_3)=8.0\times10^{-12}\) at T(K)]

  • (A) \(\sqrt{1.3\times10^{-7}}\) M
  • (B) \(\sqrt{1.5\times10^{-6}}\) M
  • (C) \(\sqrt{1.6\times10^{-6}}\) M
  • (D) \(\sqrt{1.6\times10^{-5}}\) M

Question 131:

Temperature of maximum density of H\(_2\)O is y K and D\(_2\)O is x K. (x - y) (in K) is nearly

  • (A) 7.0
  • (B) 3.5
  • (C) 4.0
  • (D) 8.5

Question 132:

How many of the following metals give oxides and nitrides when burnt in air? Be, Na, Mg, Ba, Sr, Li, K

  • (A) 2
  • (B) 3
  • (C) 4
  • (D) 5

Question 133:

Identify the incorrect order against the property given in brackets

  • (A) BeCO\(_3\) < MgCO\(_3\) < CaCO\(_3\) < SrCO\(_3\) (Thermal stability)
  • (B) BeSO\(_4\) > MgSO\(_4\) > CaSO\(_4\) > SrSO\(_4\) (Solubility in water)
  • (C) Li\(_2\)CO\(_3\) > Na\(_2\)CO\(_3\) > K\(_2\)CO\(_3\) > Rb\(_2\)CO\(_3\) (Thermal stability)
  • (D) BeCO\(_3\) > MgCO\(_3\) > CaCO\(_3\) > SrCO\(_3\) (Solubility in water)

Question 134:

Diborane on hydrolysis gives a compound X. The correct statements about X are
I. It is a tribasic acid
II. It is a weak monobasic acid
III. It has a layer structure
IV. It is highly soluble in water

  • (A) I \& III
  • (B) II \& III
  • (C) II \& IV
  • (D) I \& IV

Question 135:

Choose the correct statements about allotropes of carbon
I. Graphite has layered structure
II. Buckminster fullerene is not aromatic in nature
III. The distance between two adjacent layers in graphite is 141.5 pm
IV. The hybridization of carbons in graphite and Buckminster fullerene is same

  • (A) I \& IV
  • (B) I \& II
  • (C) II \& III
  • (D) III \& IV

Question 136:

Which of the following is a lung irritant that can lead to an acute respiratory disease in children?

  • (A) SO\(_2\)
  • (B) CO\(_2\)
  • (C) CO
  • (D) NO\(_2\)

Question 137:

Arrange the following in decreasing order of their boiling points
(A) 2-Methylbutane
(B) 2,2-Dimethylpropane
(C) Pentane
(D) Hexane

  • (A) D > C > A > B
  • (B) B > A > C > D
  • (C) D > A > C > B
  • (D) B > C > A > D

Question 138:

Which of the following is not an aromatic species?


  • (A) Cycloheptatrienyl cation
  • (B) Cyclopentadienyl anion
  • (C) Cyclooctatetraene
  • (D) Naphthalene

Question 139:

In the estimation of nitrogen by Kjeldahl's method 0.933 g of an organic compound 'X' was analyzed. Ammonia evolved was absorbed in 60 mL of 0.1 M H\(_2\)SO\(_4\). The unreacted acid requires 20 mL of 0.1 M NaOH for complete neutralization. The compound 'X' is

  • (A) C\(_6\)H\(_5\)CH\(_2\)NH\(_2\)
  • (B) C\(_6\)H\(_5\)NH\(_2\)
  • (C) CH\(_3\)CH\(_2\)NH\(_2\)
  • (D) CH\(_3-CO-NH_2\)

Question 140:

Which of the following is a least stable carbocation?

  • (A) CH\(_3\) - C\(^+\)H\(_2\)
  • (B) CH\(_2\) = C\(^+\)H
  • (C) CH\(_2\) = CH - C\(^+\)H\(_2\)
  • (D) C\(_6\)H\(_5\) - C\(^+\)H\(_2\)

Question 141:

The incorrect statement about crystals with Schottky defect is

  • (A) It is due to missing of equal number of cations and anions from lattice points
  • (B) On the whole crystal is electrically neutral
  • (C) It is shown by ionic compounds in which cation and anion are of almost same size
  • (D) Density of the crystal increases

Question 142:

Two liquids 'A' and 'B' form an ideal solution. At 300 K, the vapour pressure of a solution containing 1 mole of 'A' and 3 moles of 'B' is 550 mm Hg. At the same temperature, if one more mole of 'B' is added to the solution, the vapour pressure of solution increases to 560 mm Hg. Then the ratio of vapour pressures of A and B in their pure state is

  • (A) 1:3
  • (B) 3:1
  • (C) 2:3
  • (D) 3:2

Question 143:

The molar conductivity of acetic acid solution at infinite dilution is 390 S cm\(^2\) mol\(^{-1}\). What is the molar conductivity of 0.01 M acetic acid solution (in S cm\(^2\) mol\(^{-1}\))? (Given: \(K_a(CH_3COOH)=1.8\times10^{-5}\), assume \(1-\alpha \approx 1\))

  • (A) 10.64
  • (B) 16.54
  • (C) 51.64
  • (D) 15.64

Question 144:

The half-life of a zero order reaction A \(\rightarrow\) products, is 0.5 hour. The initial concentration of A is 4 mol L\(^{-1}\). How much time (in hr) does it take for its concentration to come from 2.0 mol L\(^{-1}\) to 1.0 mol L\(^{-1}\)?

  • (A) \(1/4\)
  • (B) \(1/8\)
  • (C) \(1/2\)
  • (D) \(1/6\)

Question 145:

Match the following The correct answer is


  • (A) A-IV, B-II, C-III, D-I
  • (B) A-III, B-I, C-IV, D-II
  • (C) A-III, B-II, C-IV, D-I
  • (D) A-IV, B-I, C-II, D-III

Question 146:

Observe the following statements
Statement - I: The choice of reducing agent for the reduction of an oxide ore can be predicted by using Ellingham diagram, a plot of \(\Delta G^\circ\) Vs T.
Statement - II: According to Ellingham diagram, metal oxide with higher \(\Delta G^\circ\) is more stable than the oxide with lower \(\Delta G^\circ\).
The correct answer is

  • (A) Both statements I and II are correct
  • (B) Statement I is correct, but statement II is not correct
  • (C) Statement I is not correct, but statement II is correct
  • (D) Both statements I and II are not correct

Question 147:

Which one of the orders is correctly matched with the property mentioned against it?

  • (A) H\(_2\)S < H\(_2\)O < H\(_2\)Se < H\(_2\)Te (Boiling point)
  • (B) N\(_2\)O < NO < N\(_2\)O\(_3\) < N\(_2\)O\(_4\) < N\(_2\)O\(_5\) (Acidic nature)
  • (C) HI < HCl < HBr < HF (Acidic nature)
  • (D) H\(_2\)O < H\(_2\)S < H\(_2\)Se < H\(_2\)Te (Bond angle)

Question 148:

Noble gas 'X' is used as a diluent for oxygen in modern diving apparatus and noble gas 'Y' is used mainly to provide an inert atmosphere in high temperature metallurgical processes. 'Y' and 'X' are respectively?

  • (A) He, Ar
  • (B) Ar, He
  • (C) He, Kr
  • (D) Ar, Kr

Question 149:

The dibasic oxoacid of phosphorus on disproportionation gives two products A and B. A and B are respectively

  • (A) HPO\(_3\), PH\(_3\)
  • (B) H\(_3\)PO\(_2\), H\(_2\)O
  • (C) H\(_3\)PO\(_4\), PH\(_3\)
  • (D) H\(_4\)P\(_2\)O\(_6\), H\(_3\)PO\(_2\)

Question 150:

The number of moles of oxalate ions oxidized by one mole of permanganate ions in acidic medium is

  • (A) 2.5
  • (B) 5.0
  • (C) 1.5
  • (D) 2.0

Question 151:

Total number of geometrical isomers possible for the complexes [NiCl\(_4\)]\(^{2-}\), [CoCl\(_2\)(NH\(_3\))\(_4\)]\(^+\), [Co(NH\(_3\))\(_3\)(NO\(_2\))\(_3\)] and [Co(NH\(_3\))\(_5\)Cl]\(^{2+}\) is

  • (A) 2
  • (B) 3
  • (C) 4
  • (D) 5

Question 152:

Match the following The correct answer is


  • (A) A-II, B-IV, C-I, D-III
  • (B) A-II, B-III, C-IV, D-I
  • (C) A-III, B-I, C-IV, D-II
  • (D) A-III, B-II, C-IV, D-I

Question 153:

Maltose on hydrolysis gives two monosaccharide units. The incorrect statement about the monosaccharides formed is

  • (A) Both are \(\alpha\)-D-glucose units only
  • (B) One is \(\alpha\)-D-glucose and second one is \(\beta\)-D-fructose
  • (C) Both are reducing sugars
  • (D) In maltose, they are joined through 1,4-glycosidic linkage

Question 154:

Identify the pair of drugs which act as antihistamines.

  • (A) Dimetapp, Seldane
  • (B) Iproniazid, Nardil
  • (C) Veronal, Valium
  • (D) Heroin, Codeine

Question 155:

Identify the product 'Y' in the given sequence of reactions. (Chlorobenzene reacts with Conc. HNO\(_3\) and Conc. H\(_2\)SO\(_4\) to give X (Major). X then reacts with (i) NaOH, 443 K and (ii) H\(^+\) to give Y.)


  • (A) Image of 2,4-Dinitrophenol
  • (B) Image of 4-Nitrophenol
  • (C) Image of Picric acid (2,4,6-trinitrophenol)
  • (D) Image of 4-Nitrobenzenesulfonic acid

Question 156:

What is 'Z' in the given set of reactions?
C\(_6\)H\(_5\)OCH\(_3\) \(\xrightarrow{HI}\) X + Y
Y \(\xrightarrow[Anhy. AlCl_3]{C_6H_6}\) Z

                           

         


  • (A) Ethylbenzene
  • (B) Benzyl chloride
  • (C) Chlorobenzene
  • (D) Toluene

Question 157:

Which of the following reactions is an example of Clemmensen reduction?

  • (A) R-CO-Cl + H\(_2 \xrightarrow{Pd/BaSO_4}\) R-CHO + HCl
  • (B) R-CHO \(\xrightarrow{(i)NH_2NH_2, (ii)KOH/Glycol}\) R-CH\(_3\)
  • (C) R-CO-OC\(_2\)H\(_5 \xrightarrow{1. DIBAL-H, 2. H_2O}\) R-CHO + C\(_2\)H\(_5\)OH
  • (D) R-CO-CH\(_3 \xrightarrow{Zn-Hg/HCl}\) R-CH\(_2\)-CH\(_3\)

Question 158:

Which of the following can undergo Hell-Volhard-Zelinsky reaction?





  • (A) Benzoic acid
  • (B) Phenylacetic acid
  • (C) Phenylacetaldehyde
  • (D) Methyl phenyl ketone

Question 159:

Which of the following has lowest pK\(_a\) value?

 





  • (A) 4-Nitrophenol
  • (B) Benzoic acid
  • (C) 4-Methoxybenzoic acid
  • (D) 4-Nitrobenzoic acid

Question 160:

The correct statements about the products B and C in the given reactions are
(Ethanol reacts with HCl/Anhy ZnCl\(_2\) to give A. A reacts with ethanolic AgCN to give B (Minor) and C (Major)).
I. B and C are functional isomers
II. With H\(_2\)|Catalyst B gives 1\(^\circ\) amine and C gives 2\(^\circ\) amine
III. B on acid hydrolysis gives formic acid and C gives C\(_3\)H\(_6\)O\(_2\)
IV. C forms isocyanate with HgO

  • (A) I \& III
  • (B) II \& III
  • (C) I, II \& IV
  • (D) II, III \& IV

TS EAMCET 2025 Important Topics

Since more than 75% of the TS EAMCET 2025 questions are usually from selective high-weightage topics, smart preparation involves major chapters of the syllabus.

Subject-Wise Important Topics for TS EAMCET 2025

Subject Important Topics
Mathematics
  • Vectors
  • Probability
  • Integration
  • Differentiation
  • Coordinate Geometry
  • Complex Numbers
  • Matrices
Physics
  • Thermodynamics
  • Current Electricity
  • Laws of Motion
  • Semiconductor Electronics
  • Ray Optics
  • Work Energy
  • Power
Chemistry
  • Chemical Bonding
  • Organic Chemistry – Basics
  • Thermodynamics
  • p-Block Elements
  • Equilibrium
  • Solutions

Colleges Accepting TS EAMCET 2025 Marks

The TS EAMCET 2025 marks are accepted by more than 200 Telangana engineering colleges, namely, renowned state universities, autonomous colleges, and private engineering colleges.

College Name Type Approx. Closing Rank (CSE)
University College of Engineering, OU (UCE OU) Government 500 – 1,200
JNTUH College of Engineering, Hyderabad 400 – 1,000
Chaitanya Bharathi Institute of Technology (CBIT) Private (Autonomous) 1,200 – 3,500
Vasavi College of Engineering 1,000 – 3,000
VNR Vignana Jyothi Institute of Engineering & Technology Private 1,500 – 4,000
Gokaraju Rangaraju Institute of Engineering & Technology 1,500 – 4,500
CVR College of Engineering 2,000 – 5,000
MVSR Engineering College 3,000 – 6,000
Malla Reddy College of Engineering & Technology 5,000 – 9,000
Kakatiya Institute of Technology & Science (KITSW) 6,000 – 10,000