AP EAPCET 2026 Engineering Question Paper for May 15 Shift 2 is available for download here. JNTUK on behalf of APSCHE conducted AP EAPCET 2026 Engineering exam on May 15 in Shift 2 from 2 PM to 5 PM. AP EAPCET 2026 Engineering consists of 160 questions for a total of 160 marks to be attempted in 3 hours.

  • AP EAPCET 2026 Engineering is divided into 3 sections- Mathematics with 80 questions and Physics and Chemistry with 40 questions each.
  • Each correct answer carries 1 mark and there is no negative marking for incorrect answer.

AP EAPCET 2026 Engineering Question Paper PDF for May 15 Shift 2

AP EAPCET 2026 Engineering Question Paper May 15 Shift 2 Download PDF Check Solutions


Question 1:

The domain of the real-valued function \[ f(x)=\cos^{-1} (\frac{2-x}{4} )+[\log(3-x)]^{-1} \]
is:

  • (A) \( (-6,2)\cup(2,3) \)
  • (B) \( [-6,2)\cup(2,3) \)
  • (C) \( (-\infty,2)\cup(2,3) \)
  • (D) \( [-6,2)\cup(2,3] \)

Question 2:

The function \[ f(x)=\sin (\log (x+\sqrt{x^2+1} ) ) \]
is

  • (A) An even function
  • (B) An odd function
  • (C) Neither even nor odd
  • (D) A periodic function

Question 3:

If \[ a_n= \sqrt{7+\sqrt{7+\sqrt{7+ s}}} \]
(\(n\) radicals), then which of the following is true?

  • (A) \(a_n>7 \quad \forall n\ge1\)
  • (B) \(a_n>3 \quad \forall n\ge1\)
  • (C) \(a_n<3 \quad \forall n\ge1\)
  • (D) \(a_n<4 \quad \forall n\ge1\)

Question 4:

Consider the system of linear equations \[ x+y+z=6, \] \[ x+2y+3z=10, \] \[ 3x+2y+\lambda z=\mu. \]
If the system has infinitely many solutions, then the value of \(\mu+\lambda\) is:

  • (A) \(12\)
  • (B) \(14\)
  • (C) \(16\)
  • (D) \(18\)

Question 5:

Let \(f,g,h\) be differentiable functions such that \[ \begin{vmatrix} f(x) & g(x) & h(x)
f'(x) & g'(x) & h'(x)
f''(x) & g''(x) & h''(x) \end{vmatrix} =0. \]
Then which of the following statements is correct?

  • (A) \(f,g,h\) are always linearly independent
  • (B) \(f,g,h\) are linearly dependent
  • (C) Exactly two of them are equal
  • (D) None of these

Question 6:

Let \(A\) be a \(3 3\) matrix such that \[ AA^{T}=I_3. \]
Then \(A\) is:

  • (A) Singular matrix
  • (B) Orthogonal matrix
  • (C) Skew-symmetric matrix
  • (D) Nilpotent matrix

Question 7:

If \[ z=\frac{(1-i)^3}{(\sqrt{3}-i)^2}, \]
then the complex conjugate of \(z\) is:

  • (A) \(\dfrac{\sqrt{3}+1}{4}+\dfrac{\sqrt{3}-1}{4}i\)
  • (B) \(\dfrac{\sqrt{3}-1}{4}+\dfrac{\sqrt{3}+1}{4}i\)
  • (C) \(\dfrac{\sqrt{3}+1}{4}-\dfrac{\sqrt{3}-1}{4}i\)
  • (D) \(\dfrac{\sqrt{3}-1}{4}-\dfrac{\sqrt{3}+1}{4}i\)

Question 8:

The locus of the point \(z=x+iy\) satisfying \[ |\frac{z-(2+i)}{z+(2-i)} |=2 \]
is:

  • (A) A circle
  • (B) A parabola
  • (C) An ellipse
  • (D) A straight line

Question 9:

If \[ \cos\alpha+\cos\beta+\cos\gamma=0 \]
and \[ \sin\alpha+\sin\beta+\sin\gamma=0, \]
then which of the following is true?

  • (A) \(\alpha+\beta+\gamma=\pi\)
  • (B) \(\alpha+\beta+\gamma=2\pi\)
  • (C) \(\alpha,\beta,\gamma\) are angles of a triangle
  • (D) One of the angles differs from another by \(180^\circ\)

Question 10:

Let \(\alpha\) and \(\beta\) be the roots of \[ x^2+bx+c=0. \]
If \[ \alpha^2+\beta^2=14 \]
and \[ \alpha\beta=3, \]
then the value of \(b^2\) is:

  • (A) \(8\)
  • (B) \(16\)
  • (C) \(20\)
  • (D) \(28\)

Question 11:

The number of integers that satisfy both the inequalities \[ x^2-2x+8>0 \]
and \[ x^2-3x+2\le 0 \]
is:

  • (A) \(1\)
  • (B) \(2\)
  • (C) \(4\)
  • (D) Infinite

Question 12:

2 is a zero of the polynomial function \[ f(x)=x^4+kx^3+22x^2-6x-20. \]
If \(-2,\alpha,\beta\) are the roots of the equation \[ x^3+3x^2+2kx-40=0 \]
and \(\alpha<\beta\), then \(2\alpha+3\beta=\)

  • (A) \(1\)
  • (B) \(2\)
  • (C) \(5\)
  • (D) \(8\)

Question 13:

If \(5\) is the remainder when \[ 2x^5+kx^4+5x^3-3x^2+2x-1 \]
is divided by \[ x^2+x+1, \]
then the quotient is:

  • (A) \(2x^3-x^2+10x+4\)
  • (B) \(2x^3-5x^2+8x-6\)
  • (C) \(2x^3-5x^2+10x+4\)
  • (D) \(2x^3-x^2+8x-6\)

Question 14:

If \[ {}^{n}P_{4}=5040 \]
and \[ {}^{15}P_{r}=2730, \]
then the value of \(n+r\) is:

  • (A) \(10\)
  • (B) \(12\)
  • (C) \(14\)
  • (D) \(16\)

Question 15:

The number of arrangements of the letters of the word SEARCH such that no letter remains in its original position is:

  • (A) \(264\)
  • (B) \(265\)
  • (C) \(266\)
  • (D) \(267\)

Question 16:

If the coefficients of the first, second, and third terms in the expansion of \( (1+x)^n \) are in the ratio \(1:20:190\), then \(n\) is equal to:

  • (A) \(18\)
  • (B) \(19\)
  • (C) \(20\)
  • (D) \(21\)

Question 17:

If \(\alpha,\beta\) are the roots of the quadratic equation \[ x^2-3x+1=0, \]
then the value of \(\alpha^3+\beta^3\) is:

  • (A) \(9\)
  • (B) \(18\)
  • (C) \(21\)
  • (D) \(27\)

Question 18:

If the coefficient of \(x^2\) in the expansion of \[ (1+x)^5(1-x)^4 \]
is \(k\), then \(k\) is equal to:

  • (A) \(-10\)
  • (B) \(-5\)
  • (C) \(0\)
  • (D) \(10\)

Question 19:

If \[ \sin +\cos =1, \]
then the value of \[ \sin \cos \]
is:

  • (A) \(-1\)
  • (B) \(0\)
  • (C) \(\frac12\)
  • (D) \(1\)

Question 20:

If \[ \log_2(x-1)+\log_2(x+1)=3, \]
then \(x\) is equal to:

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

Question 21:

If \[ f(x)=|x-2|+|x+1|, \]
then the minimum value of \(f(x)\) is:

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

Question 22:

If the arithmetic mean of the numbers \[ 2,4,6,\ldots,2n \]
is \(\frac{7}{4}\), then \(n\) is equal to:

  • (A) \(1\)
  • (B) \(\frac34\)
  • (C) \(\frac54\)
  • (D) \(\frac74\)

Question 23:

If \[ z=\cos +i\sin , \]
then \(|z|\) is equal to:

  • (A) \(0\)
  • (B) \(1\)
  • (C) \(\sqrt2\)
  • (D) \(\sqrt3\)

Question 24:

If \[ A= \begin{bmatrix} 1&2
3&4 \end{bmatrix}, \]
then \(\det(A)\) is equal to:

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

Question 25:

If \[ \log_a 2+\log_a 5=1, \]
then the value of \(a\) is:

  • (A) \(7\)
  • (B) \(10\)
  • (C) \(12\)
  • (D) \(15\)

Question 26:

The distance between the points \[ (1,2) \quad and \quad (4,6) \]
is:

  • (A) \(3\)
  • (B) \(4\)
  • (C) \(5\)
  • (D) \(6\)

Question 27:

If \[ x+\frac1x=3, \]
then the value of \[ x^2+\frac1{x^2} \]
is:

  • (A) \(5\)
  • (B) \(7\)
  • (C) \(9\)
  • (D) \(11\)

Question 28:

The ratio in which the point \[ (3,4) \]
divides the line segment joining \[ (1,2) \]
and \[ (5,6) \]
is:

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

Question 29:

If \[ \vec a=2\hat i+\hat j-\hat k \]
and \[ \vec b=\hat i-2\hat j+3\hat k, \]
then the value of \[ \vec a+\vec b \]
is:

  • (A) \(3\hat i-\hat j+2\hat k\)
  • (B) \(3\hat i+\hat j+2\hat k\)
  • (C) \(\hat i-3\hat j+4\hat k\)
  • (D) \(3\hat i-3\hat j+4\hat k\)

Question 30:

Let \(\vec a,\vec b\) be two non-collinear vectors. If \[ \vec r=(x+2y-3)\vec a+(2x-y+1)\vec b \]
and \[ \vec R=(3x-y-2)\vec a+(x+3y+2)\vec b \]
are vectors such that \[ 2\vec r=m\vec R, \]
then \(x+5y=\)

  • (A) \(4\)
  • (B) \(6\)
  • (C) \(9\)
  • (D) \(8\)

Question 31:

The shortest distance between the lines \[ \vec r=\vec a+t\vec b \]
and \[ \vec r=\vec c+s\vec d \]
where \[ \vec a=\hat i-2\hat j+2\hat k, \quad \vec b=3\hat i-2\hat j-2\hat k, \] \[ \vec c=6\hat i+2\hat j+2\hat k, \quad \vec d=-4\hat i-\hat k, \]
is

  • (A) \(9\)
  • (B) \(\dfrac{6\sqrt3}{\sqrt7}\)
  • (C) \(\dfrac{\sqrt7}{2\sqrt3}\)
  • (D) \(\dfrac{5}{\sqrt3}\)

Question 32:

If \[ |\vec a|=2k, \qquad |\vec b|=k \]
and \[ |\vec a-\vec b|^2=20k^2-|2\vec a+\vec b|^2, \]
then \[ |\vec a \vec b| = \ ? \]

  • (A) \(\sqrt3\,k^2\)
  • (B) \(k^2\)
  • (C) \(2\sqrt3\,k^2\)
  • (D) \(2k^2\)

Question 33:

Given that \[ \vec a=2\hat i-\hat j+2\hat k,\qquad \vec b=\hat i-2\hat j+2\hat k,\qquad \vec c=2\hat i-2\hat j-\hat k, \]
if \(\vec d\) is a vector perpendicular to the plane containing \(\vec a,\vec b,\vec c\) and \[ |\vec d-\vec c|=2, \]
then \[ |(\vec d-\vec c) (\vec a \vec b)|= \]

  • (A) \(16\)
  • (B) \(4\sqrt2\)
  • (C) \(8\)
  • (D) \(8\sqrt2\)

Question 34:

The variance of the following frequency distribution is


  • (A) \(264\)
  • (B) \(88\)
  • (C) \(84\)
  • (D) \(90\)

Question 35:

If it is known that a woman has two children and she has at least one girl child, then the probability that both children are girls is

  • (A) \(\frac13\)
  • (B) \(\frac14\)
  • (C) \(\frac12\)
  • (D) \(\frac23\)

Question 36:

From the set of numbers \[ \{1,2,3,4,5,6,7,8,9,10,11,12\}, \]
two numbers are selected at random. The probability that the two numbers selected differ by a prime number is

  • (A) \(\frac{16}{33}\)
  • (B) \(\frac{1}{11}\)
  • (C) \(\frac{3}{11}\)
  • (D) \(\frac{11}{24}\)

Question 37:

A bag \(P\) contains \(5\) white and \(4\) blue balls. Another bag \(Q\) contains \(4\) white and \(5\) blue balls. One ball is drawn at random from bag \(P\) and transferred to another bag. Then one ball is drawn from bag \(Q\). Find the probability that the ball drawn from bag \(Q\) has the same colour as the ball transferred from bag \(P\).

  • (A) \(\frac{2}{9}\)
  • (B) \(\frac{1}{9}\)
  • (C) \(\frac{5}{9}\)
  • (D) \(\frac{4}{9}\)

Question 38:

In a sample space, \(E\) is an event associated with the events \(A\) and \(B\). If \[ P(A|E)=l \]
and \[ P(E|B)=m, \]
then \(P(B|E)\) is

  • (A) \[ \frac{m}{1+m} \] always
  • (B) \[ \frac{1}{1+m} \] only when \(P(A)+P(B)=1\)
  • (C) \[ \frac{m}{1+m} \] only when \(P(A)+P(B)=1\)
  • (D) \[ \frac{1}{1+m} \] always

Question 39:

If the probability function of a random variable \(X\) is \[ P(X=x)=ak^x,\qquad x=0,1,2,\ldots, \]
then the value of \(k\) is

  • (A) (1-a,;0
  • (B) \(1-a\) for all positive \(a\)
  • (C) \(\dfrac{1}{1-a}\)
  • (D) \(a-1\)

Question 40:

If \[ X\sim B\! (n,\frac14 ), \] \[ P(X=2)=P(X=3) \]
and \[ \sum_{k=0}^{2}P(X=k)=\frac{39}{411}, \]
then \(n=\)

  • (A) \(97\)
  • (B) \(38\)
  • (C) \(128\)
  • (D) \(152\)

Question 41:

The locus of the point which forms a right-angled triangle with the fixed points \((2,3)\) and \((5,1)\) is

  • (A) A circle or a pair of parallel lines
  • (B) A pair of parallel lines which are parallel to the line joining the given points
  • (C) A circle having the line joining the given points as a chord
  • (D) The perpendicular bisector of the line joining the given points

Question 42:

The equation of the normal to the parabola \[ y^2=12x \]
at the point \((3\lambda^2,6\lambda)\) is

  • (A) \[ y=-\lambda x+6\lambda+3\lambda^3 \]
  • (B) \[ y=-\lambda x+6\lambda+3\lambda^2 \]
  • (C) \[ y=-2\lambda x+6\lambda+3\lambda^3 \]
  • (D) \[ y=-\lambda x+3\lambda+6\lambda^3 \]

Question 43:

The equation of the tangent to the ellipse \[ \frac{x^2}{16}+\frac{y^2}{9}=1 \]
which is parallel to the line \[ 3x+4y+5=0 \]
is

  • (A) \[ 3x+4y=\pm 20 \]
  • (B) \[ 3x+4y=\pm 15 \]
  • (C) \[ 3x+4y=\pm 12 \]
  • (D) \[ 3x+4y=\pm 25 \]

Question 44:

The eccentricity of the hyperbola \[ 16x^2-9y^2=144 \]
is

  • (A) \(\dfrac{5}{4}\)
  • (B) \(\dfrac{3}{2}\)
  • (C) \(\dfrac{4}{3}\)
  • (D) \(\dfrac{5}{3}\)

Question 45:

If the equation \[ x^2-6x+y^2+8y+9=0 \]
represents a circle, then its radius is:

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

Question 46:

If \[ _0^1 (3x^2+2x+1)\,dx=k, \]
then the value of \(k\) is

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

Question 47:

If the equation \[ 2x^2-5x+k=0 \]
has equal roots, then the value of \(k\) is

  • (A) \(\dfrac{25}{8}\)
  • (B) \(\dfrac{8}{25}\)
  • (C) \(\dfrac{25}{4}\)
  • (D) \(\dfrac{5}{2}\)

Question 48:

If \[ \log_2(x-1)+\log_2(x-3)=3, \]
then the value of \(x\) is

  • (A) \(5\)
  • (B) \(1+\sqrt{17}\)
  • (C) \(4+\sqrt{5}\)
  • (D) \(3+\sqrt{17}\)

Question 49:

The value of \[ \sin^2 15^\circ+\cos^2 15^\circ \]
is

  • (A) \(0\)
  • (B) \(\dfrac12\)
  • (C) \(1\)
  • (D) \(\sqrt2\)

Question 50:

If the pole of the line \[ 2x+3y-20=0 \]
with respect to the circle \[ x^2+y^2-4x+6y-12=0 \]
is \((\alpha,\beta)\), then the number of tangents that can be drawn from \((\alpha,\beta)\) to the given circle is:

  • (A) \(\beta\)
  • (B) \(\alpha-2\)
  • (C) \(\beta+1\)
  • (D) \(\alpha\)

Question 51:

The centre of the circle which intersects the circles \[ x^2+y^2-8x+10y+5=0 \]
and \[ x^2+y^2-2x+2y+1=0 \]
orthogonally is:

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

Question 52:

If \[ y=mx+\frac{3}{m} \]
is a tangent to the parabola \[ y^2=4ax \]
at the point \(P(3,\beta)\), where \(\beta<0\), then the value of \[ 3m-\beta \]
is:

  • (A) \(2a\)
  • (B) \(ma\)
  • (C) \(a\)
  • (D) \(\dfrac{|\beta|}{a}\)

Question 53:

The product of the slopes of the non-horizontal normals drawn through the point \[ (6,0) \]
to the parabola \[ y^2=8x \]
is:

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

Question 54:

If the ends of the major axis \(A'\) and \(A\) of the ellipse \[ \frac{(x-2)^2}{a^2}+\frac{(y-3)^2}{b^2}=1 \]
are respectively at distances \(9\) and \(3\) units from a directrix \(L\), then the foci of the ellipse are:

  • (A) \( (2\pm\frac34,\;3 )\)
  • (B) \( (2\pm\frac32,\;3 )\)
  • (C) \( (\pm\frac32,\;3 )\)
  • (D) \( (\pm\frac34,\;3 )\)

Question 55:

Consider the hyperbola \[ S \equiv \frac{x^2}{25}-\frac{y^2}{16}-1=0. \]
Let \(B,B'\) be the ends of the transverse axis of the conjugate hyperbola of \(S=0\). If \(C\) is the circle with \(B,B'\) as ends of a diameter, then the slope of a common tangent to \(C\) and the given hyperbola is:

  • (A) \(\pm \dfrac{3\sqrt2}{4}\)
  • (B) \(\pm \dfrac{4\sqrt2}{3}\)
  • (C) \(\pm \dfrac{5\sqrt3}{4}\)
  • (D) \(\pm \dfrac{3\sqrt3}{2}\)

Question 56:

Let \[ O(0,0,0) \]
and \[ A(2,1,-3) \]
be vertices of a triangle \(OAB\). If \[ (-1,2,1) \]
is the midpoint of side \(AB\), and the perimeter of the triangle is \[ \sqrt2\,(k+l\sqrt7+m\sqrt{13}), \]
then the value of \[ k+l+m \]
is:

  • (A) \(7\)
  • (B) \(8\)
  • (C) \(5\)
  • (D) \(6\)

Question 57:

If the feet of the perpendiculars drawn from the point \[ (3,4,5) \]
to the \(X\)-, \(Y\)- and \(Z\)-coordinate axes are \(A,B,C\) respectively and the angle between \(AB\) and \(AC\) is \[ \cos^{-1} (\frac{9}{a} ), \]
then the value of \(a\) is:

  • (A) \(5\sqrt{34}\)
  • (B) \(3\sqrt{34}\)
  • (C) \(2\sqrt{34}\)
  • (D) \(\sqrt{34}\)

Question 58:

Let \( \) be the angle between the line \[ \frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2} \]
and the plane \[ 2x-y+\sqrt{\lambda}\,z+4=0. \]

If
\[ \sin =\frac13, \]

then the value of \(\lambda\) is:

  • (A) \(\dfrac43\)
  • (B) \(\dfrac53\)
  • (C) \(\dfrac23\)
  • (D) \(\dfrac73\)

Question 59:

Let \[ \vec a=\hat i+2\hat j+2\hat k, \qquad \vec b=2\hat i+\hat j+2\hat k. \]

If \( \) is the angle between \(\vec a\) and \(\vec b\), then the value of \[ \cos \]
is:

  • (A) \(\frac{8}{9}\)
  • (B) \(\frac{7}{9}\)
  • (C) \(\frac{5}{9}\)
  • (D) \(\frac{4}{9}\)

Question 60:

Let \[ A= \begin{bmatrix} 1 & 2
2 & 1 \end{bmatrix}. \]

Then the determinant of \(A^2\) is:

  • (A) \(9\)
  • (B) \(16\)
  • (C) \(25\)
  • (D) \(36\)

Question 61:

If \[ \sin +\cos =\sqrt{2}\cos\alpha, \]
where \(0< <\frac{\pi}{2}\), then the value of \[ \sin2 \]
is:

  • (A) \(\cos2\alpha\)
  • (B) \(\sin2\alpha\)
  • (C) \(1-\cos2\alpha\)
  • (D) \(2\cos^2\alpha-1\)

Question 62:

The value of \[ \lim_{x\to0}\frac{\sin5x-5\sin x}{x^3} \]
is:

  • (A) \(-20\)
  • (B) \(-10\)
  • (C) \(10\)
  • (D) \(20\)

Question 63:

If \[ \tan +\cot =4, \]
then the value of \[ \sec^2 +\csc^2 \]
is:

  • (A) \(14\)
  • (B) \(16\)
  • (C) \(18\)
  • (D) \(20\)

Question 64:

The value of \[ \sin20^\circ\sin40^\circ\sin80^\circ \]
is:

  • (A) \(\frac18\)
  • (B) \(\frac{\sqrt3}{8}\)
  • (C) \(\frac14\)
  • (D) \(\frac{\sqrt3}{4}\)

Question 65:

If the displacement of a particle at time \(t\) (\(0 < t < \pi\)) is given by \(s = 3 \sin 2t - 6 \cos t\), then the acceleration for the values of \(t\) at which its velocity is zero is:

  • (A) \(0 units/sec^2\)
  • (B) \(2 units/sec^2\)
  • (C) \(3 units/sec^2\)
  • (D) \(4 units/sec^2\)

Question 66:

If \(f(x) = \sqrt{3}\sin x - \cos x - 2ax + b\) decreases for all \(x \in \mathbb{R}\), then:

  • (A) \(a \le 1\)
  • (B) \(a \ge 1\)
  • (C) \(a \le \frac{1}{2}\)
  • (D) \(a \ge \frac{1}{2}\)

Question 67:

The maximum area of a rectangle inscribed in a circle of radius \(r\) is:

  • (A) \(\frac{3r}{4}\)
  • (B) \(r^2\)
  • (C) \(\frac{r^2}{4}\)
  • (D) \(2r^2\)

Question 68:

The maximum value of \(y = x(\log x)^2\) is:

  • (A) \(e^{-2}\)
  • (B) \(2e^{-2}\)
  • (C) \(4e^{-2}\)
  • (D) \(5e^{-2}\)

Question 69:

Evaluate \( \frac{1+x^2}{\sqrt{1-x^2}} dx\):

  • (A) \(\frac{3}{2}\sin^{-1}x - \frac{x}{2}\sqrt{1-x^2}+c\)
  • (B) \(\frac{3}{2}\sin^{-1}x + \frac{x}{2}\sqrt{1-x^2}+c\)
  • (C) \(\frac{1}{2}\sin^{-1}x - \frac{x}{2}\sqrt{1-x^2}+c\)
  • (D) \(\frac{1}{2}\sin^{-1}x + \frac{x}{2}\sqrt{1-x^2}+c\)

Question 70:

Evaluate \( \frac{x-1}{(x+1)^3}e^x dx\):

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

Question 71:

The evaluation of the indefinite integral \( \frac{dx}{\sin x + \sin 2x}\) is:

  • (A) \(\frac{1}{4}\log|1-\cos x| + \frac{1}{3}\log|1+\cos x| - \frac{2}{3}\log|1+2\cos x| + c\)
  • (B) \(\frac{1}{3}\log|1-\cos x| + \frac{1}{4}\log|1+\cos x| + \frac{1}{3}\log|1+2\cos x| + c\)
  • (C) \(\frac{1}{6}\log|1-\cos x| + \frac{1}{2}\log|1+\cos x| - \frac{2}{3}\log|1+2\cos x| + c\)
  • (D) \(\frac{1}{6}\log|1-\cos x| + \frac{1}{4}\log|1+\cos x| + \frac{2}{3}\log|1+2\cos x| + c\)

Question 72:

If \( \frac{\cos 8x + 1}{\cot 2x - \tan 2x} dx = A\cos 8x + c\), then \(A =\)

  • (A) \(-\frac{1}{16}\)
  • (B) \(\frac{1}{16}\)
  • (C) \(-\frac{1}{8}\)
  • (D) \(\frac{1}{8}\)

Question 73:

If \( x^5 e^{-4x^3} dx = \frac{1}{48}e^{-4x^3} f(x) + c\), then \(f(x) =\)

  • (A) \(-2x^3 - 1\)
  • (B) \(-4x^3 - 1\)
  • (C) \(-2x^2 + 1\)
  • (D) \(4x^3 + 1\)

Question 74:

Evaluate \(\lim_{n\to\infty} \frac{1}{n^2}\sum_{r=1}^n r e^{r/n}\)

  • (A) \(0\)
  • (B) \(1\)
  • (C) \(e\)
  • (D) \(2e\)

Question 75:

Area between \(y^2=x\) and \(y=|x|\) is:

  • (A) \(\frac{1}{6}\)
  • (B) \(\frac{1}{3}\)
  • (C) \(\frac{1}{2}\)
  • (D) \(\frac{2}{3}\)

Question 76:

Evaluate \( _{-\pi}^{\pi} \frac{\cos^2 x}{1+a^x} dx\)

  • (A) \(a\pi\)
  • (B) \(\frac{\pi}{a}\)
  • (C) \(\frac{\pi}{2}\)
  • (D) \(2\pi\)

Question 77:

Evaluate \( _0^{\pi/2} \sin^6 x \cos^4 x dx\)

  • (A) \(\frac{8}{693}\)
  • (B) \(\frac{\pi}{128}\)
  • (C) \(\frac{3\pi}{512}\)
  • (D) \(\frac{3\pi}{256}\)

Question 78:

Eliminate constants from \(y=A(x+B)^2\)

  • (A) \(2yy''=(y')^2\)
  • (B) \(yy''=2y'\)
  • (C) \(2yy''=y'+y\)
  • (D) \(2yy''=y'-y\)

Question 79:

Solve \(\cos(x+y)dy=dx\)

  • (A) \(y=\tan\frac{x+y}{2}+c\)
  • (B) \(y=x\sec(y/x)+c\)
  • (C) \(y=-\cos^{-1}(y/x)+c\)
  • (D) \(y=\tan(x+y)+c\)

Question 80:

Solve \((1+y^2)+(x-e^{-\tan^{-1}y})\frac{dy}{dx}=0\)

  • (A) \(xe^{\tan^{-1}y}=\tan^{-1}y+c\)
  • (B) \(x^2e^{2\tan^{-1}y}=e^{\tan^{-1}y}+c\)
  • (C) \((x-2)=ce^{-\tan^{-1}y}\)
  • (D) \(2xe^{\tan^{-1}y}=e^{2\tan^{-1}y}+c\)

Question 81:

The range of strong nuclear force is in the order of:

  • (A) \(Infinity\) 
  • (B) \(\sim 10^{-16} m\) 
  • (C) \(Zero\) 
  • (D) \(\sim 10^{-15} m\)

Question 82:

Acceleration varies as \(a = 6t\). Starting from rest, the velocity of the particle after \(t = 2 s\) is:

  • (A) \(6 ms^{-1}\) 
  • (B) \(12 ms^{-1}\) 
  • (C) \(18 ms^{-1}\) 
  • (D) \(24 ms^{-1}\)

Question 83:

A projectile is projected from a moving truck. Its range depends on:

  • (A) Truck velocity only 
  • (B) Projectile velocity with respect to truck only 
  • (C) Projectile velocity with respect to ground 
  • (D) Projectile mass

Question 84:

An object is projected from the top of a tower of height \(H\) at an angle \( \) with the horizontal. It strikes the ground at \(P\) lying at a distance \(D\) from the foot of the tower. Calculate the maximum height attained by the object from the ground level:


  • (A) \(\frac{v^{2}\sin^{2} }{2g}\) 
  • (B) \(H+\frac{D^{2}\tan^{2} }{4(H+D \tan )}\) 
  • (C) \(H+D\tan \) 
  • (D) \(H+\frac{D^{2}}{v \cos }\)

Question 85:

A particle moves in a horizontal circle. If its speed is doubled, the centripetal force acting on it becomes:

  • (A) Same 
  • (B) Double 
  • (C) Four times 
  • (D) Half

Question 86:

A \(5 kg\) block on a horizontal surface is pulled by a force of \(15 N\). If the coefficient of friction between the block and the surface is \(0.2\), then the acceleration of the block is [Take \(g = 10 ms^{-2}\)]:

  • (A) \(0 ms^{-2}\) 
  • (B) \(1 ms^{-2}\) 
  • (C) \(2 ms^{-2}\) 
  • (D) \(3 ms^{-2}\)

Question 87:

A body which is initially at rest breaks into 2 pieces of masses \(4M\) and \(6M\) respectively, together having a total kinetic energy \(E\). The piece with mass \(4M\), after breaking has a kinetic energy of:

  • (A) \(0.6 E\) 
  • (B) \(0.4 E\) 
  • (C) \(0.2 E\) 
  • (D) \(0.8 E\)

Question 88:

A moving block having mass \(m\) collides with another stationary block of mass \(5m\). After the collision, the block with mass \(m\) comes to rest. If the initial velocity of the block with mass \(m\) is \(V\), then the value of the coefficient of restitution (\(e\)) is:

  • (A) \(0.2\) 
  • (B) \(0.5\) 
  • (C) \(0.7\) 
  • (D) \(0.25\)

Question 89:

A particle executes uniform circular motion with an angular momentum \(L\). If its kinetic energy is doubled and the angular frequency is halved, then its angular momentum becomes:

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

Question 90:

Two identical particles move towards each other with velocities \(2V\) and \(V\) respectively. The velocity of the center of mass of this system is:

  • (A) \(V\) 
  • (B) \(\frac{V}{3}\) 
  • (C) \(\frac{V}{2}\) 
  • (D) \(\frac{V}{4}\)

Question 91:

The springs are connected to the blocks as shown in figures A and B. When the blocks are slightly displaced and released, they oscillate with time periods T_A and T_B respectively. Then, the value of {T_A}{T_B} is:


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

Question 92:

The energy of a particle executing SHM is given by E = Ax^2 + BV^2. The INCORRECT statement is:

  • (A) Amplitude is sqrt{frac{E}{A}}
  • (B) Maximum velocity is sqrt{frac{E}{B}}
  • (C) Time period is 2pisqrt{frac{B}{A}}
  • (D) Maximum acceleration is frac{sqrt{EA}}{B}

Question 93:

A planet revolves around the sun in an elliptical orbit. The areal velocity is 4 10^{16} m^2s^{-1}. Maximum distance is 4 10^{12} m. Find minimum speed.

  • (A) 1 10^4 ms^{-1}
  • (B) 2 10^4 ms^{-1}
  • (C) 4 10^4 ms^{-1}
  • (D) 8 10^4 ms^{-1}

Question 94:

Work done in stretching a wire of length L, area A, Young's modulus Y by x is:

  • (A) frac{YAx}{L}
  • (B) frac{YAx^2}{L}
  • (C) frac{YAx^2}{2L}
  • (D) frac{2YAx^2}{L}

Question 95:

Terminal velocity of a small sphere falling in viscous liquid varies with radius as:

  • (A) v_t propto r
  • (B) v_t propto r^2
  • (C) v_t propto frac{1}{r}
  • (D) v_t propto frac{1}{r^2}

Question 96:

Equal masses of two substances of densities rho_1 and rho_2 are mixed. Density of mixture is:

  • (A) frac{rho_1 + rho_2}{2}
  • (B) frac{2rho_1rho_2}{rho_1 + rho_2}
  • (C) frac{rho_1rho_2}{rho_1 + rho_2}
  • (D) frac{rho_1 + rho_2}{2rho_1rho_2}

Question 97:

The fraction of the total volume occupied by atoms in a Simple Cubic (SC) structure is:

  • (A) \( \frac{\pi}{6} \)
  • (B) \( \frac{\pi}{4} \)
  • (C) \( \frac{\pi}{3\sqrt{2}} \)
  • (D) \( \frac{\pi}{3\sqrt{3}} \)

Question 98:

The average kinetic energy of a molecule of a perfect gas at temperature T is given by:

  • (A) \( \frac{1}{2} k_B T \)
  • (B) \( \frac{3}{2} k_B T \)
  • (C) \( k_B T \)
  • (D) \( 2 k_B T \)

Question 99:

The efficiency of a Carnot engine working between temperatures \(T_1\) and \(T_2\) (where \(T_1 > T_2\)) is given by:

  • (A) \( \eta = 1 - \frac{T_1}{T_2} \)
  • (B) \( \eta = 1 - \frac{T_2}{T_1} \)
  • (C) \( \eta = \frac{T_1}{T_2} - 1 \)
  • (D) \( \eta = \frac{T_2}{T_1} \)

Question 100:

An ideal gas is taken through a cyclic process ABCA shown in a P–V diagram. The net work done by the gas during the complete cycle is:


  • (A) \( 4 P_0 V_0 \)
  • (B) \( 2 P_0 V_0 \)
  • (C) \( P_0 V_0 \)
  • (D) \( 6 P_0 V_0 \)

Question 101:

{The temperature of a given mass of an ideal gas is changed from 27^circ C to 327^circ C at constant pressure. If the initial volume of the gas is V, then its final volume will be:

  • (A) 2V 
  • (B) 3V 
  • (C) 4V 
  • (D) frac{V}{2}

Question 102:

The mean free path lambda of a gas molecule of diameter d and number density n (number of molecules per unit volume) is inversely proportional to:

  • (A) n d 
  • (B) n^2 d 
  • (C) n d^2 
  • (D) sqrt{n} d

Question 103:

A string of mass 2.5 kg is under a tension of 200 N. The length of the stretched string is 20 m. If a transverse jerk is struck at one end of the string, the time taken for the disturbance to reach the other end is:

  • (A) 0.5 s 
  • (B) 1.0 s 
  • (C) 0.25 s 
  • (D) 2.0 s

Question 104:

The equation of a simple harmonic progressive wave is given by y = 0.05 sin(100pi t - 0.4pi x), where x and y are in meters and t is in seconds. The wave velocity is:

  • (A) 250 ms^{-1}
  • (B) 100 ms^{-1}
  • (C) 50 ms^{-1}
  • (D) 25 ms^{-1}

Question 105:

The terminal velocity v of a small spherical ball of radius r falling through a viscous liquid is directly proportional to:

  • (A) \( r \)
  • (B) \( r^2 \)
  • (C) \( \frac{1}{r} \)
  • (D) \( \frac{1}{r^2} \)

Question 106:

If the absolute temperature of a black body is tripled, the total radiant energy emitted per second per unit area increases by a factor of:

  • (A) 3
  • (B) 9
  • (C) 27
  • (D) 81

Question 107:

The fundamental frequency of a closed organ pipe of length L is equal to the frequency of the first overtone of an open organ pipe of length L'. The relation between their lengths is:

  • (A) \( L' = 4L \)
  • (B) \( L' = 2L \)
  • (C) \( L = L' \)
  • (D) \( L' = \frac{L}{2} \)

Question 108:

Two sound waves having wavelengths 5.0 m and 5.5 m respectively produce 10 beats per second when propagating in a gas. The velocity of sound in the gas is:


  • (A) 330 ms\(^{-1}\)
  • (B) 550 ms\(^{-1}\)
  • (C) 1100 ms\(^{-1}\)
  • (D) 220 ms\(^{-1}\)

Question 109:

The energy of a particle executing Simple Harmonic Motion (SHM) is given by E = Ax^2 + BV^2. Here 'x' is the displacement of the particle from its mean position, 'V' is its velocity at 'x', and A and B are positive constants. The maximum velocity of the particle is:


  • (A) \( \sqrt{\frac{E}{B}} \)
  • (B) \( \sqrt{\frac{E}{A}} \)
  • (C) \( \sqrt{\frac{2E}{B}} \)
  • (D) \( \sqrt{\frac{2E}{A}} \)

Question 110:

A planet revolves around the Sun in an elliptical orbit. The areal velocity of the planet is \(4 10^{16}\,m^2s^{-1}\). If the maximum distance between the planet and the Sun is \(4 10^{12}\,m\), then the minimum speed of the planet is:


  • (A) \( 1 10^4\,m s^{-1} \)
  • (B) \( 2 10^4\,m s^{-1} \)
  • (C) \( 4 10^4\,m s^{-1} \)
  • (D) \( 8 10^4\,m s^{-1} \)

Question 111:

The structural characteristics of Simple Harmonic Motion (SHM) require that the acceleration of a particle is directly proportional to its displacement from the mean position and is directed:


  • (A) along the direction of motion
  • (B) opposite to the direction of velocity at all times
  • (C) towards the mean position
  • (D) away from the mean position

Question 112:

The displacement of a progressive wave is given by \( y = 0.5 \sin(100t - 2x) \), where x and y are in meters and t is in seconds. The velocity of the wave is:

  • (A) \( 25\,m s^{-1} \)
  • (B) \( 50\,m s^{-1} \)
  • (C) \( 100\,m s^{-1} \)
  • (D) \( 200\,m s^{-1} \)

Question 113:

The electric potential at a point on the axis of an electric dipole at a distance r from its center is proportional to:

  • (A) \( \frac{1}{r} \)
  • (B) \( \frac{1}{r^2} \)
  • (C) \( \frac{1}{r^3} \)
  • (D) \( r^2 \)

Question 114:

Three capacitors of capacitances \(2\,\mu F\), \(3\,\mu F\), and \(6\,\mu F\) are connected in series. The equivalent capacitance is:

  • (A) \( 11\,\mu F \)
  • (B) \( 1\,\mu F \)
  • (C) \( 0.5\,\mu F \)
  • (D) \( 2\,\mu F \)

Question 115:

A wire of resistance R is stretched uniformly to double its original length. The new resistance will be:

  • (A) \( 2R \)
  • (B) \( 4R \)
  • (C) \( \frac{R}{2} \)
  • (D) \( \frac{R}{4} \)

Question 116:

The threshold frequency for a certain photosensitive metal surface is nu_0. When light of frequency 2nu_0 is incident on the surface, the maximum velocity of the emitted photoelectrons is v_1. If the frequency is increased to 5nu_0, the maximum velocity becomes v_2. The ratio v_1 : v_2 is:

  • (A) (A) \(1:2\)
  • (B) (B) \(1:4\)
  • (C) (C) \(2:1\)
  • (D) (D) \(1:\sqrt{2}\)

Question 117:

In a nuclear reactor, heavy water (D_2O) is used as a moderator. Its main function is to:

  • (A) (A) absorb neutrons to stop reaction
  • (B) (B) accelerate neutrons to sustain reaction
  • (C) (C) slow down fast neutrons to thermal energies
  • (D) (D) cool the reactor core

Question 118:

Doping a semiconductor with a trivalent impurity results in:

  • (A) (A) p-type semiconductor
  • (B) (B) n-type semiconductor
  • (C) (C) intrinsic semiconductor
  • (D) (D) perfect insulator

Question 119:

In an electromagnetic wave in vacuum, the relation between peak electric field E_0 and magnetic field B_0 is:


  • (A) (A) \(E_0 = B_0\)
  • (B) (B) \(B_0 = cE_0\)
  • (C) (C) \(E_0 = cB_0\)
  • (D) (D) \(E_0 = c^2B_0\)

Question 120:

For a convex lens, magnifications m_1 and m_2 correspond to object distances u_1 and u_2. The focal length is:

  • (A) (A) \(\frac{u_2 - u_1}{m_1 - m_2}\)
  • (B) (B) \(\frac{m_1 m_2 (u_1 - u_2)}{m_2 - m_1}\)
  • (C) (C) \(\frac{u_1 - u_2}{m_2 - m_1}\)
  • (D) (D) \(\frac{u_2 - u_1}{m_2 - m_1}\)

Question 121:

Which quantum number combination is impossible for a hydrogenic atom orbital?

  • (A) (A) \(n = 3, l = 2, m_l = -2, m_s = +\frac{1}{2}\)
  • (B) (B) \(n = 4, l = 0, m_l = 0, m_s = -\frac{1}{2}\)
  • (C) (C) \(n = 3, l = 3, m_l = +1, m_s = +\frac{1}{2}\)
  • (D) (D) \(n = 2, l = 1, m_l = 0, m_s = -\frac{1}{2}\)

Question 122:

Correct increasing order of first ionization enthalpy is: C, O, N, F

  • (A) (A) C < N < O < F
  • (B) (B) C < O < N < F
  • (C) (C) O < C < N < F
  • (D) (D) C < O < F < N

Question 123:

Which species has bond order 2.5 and is paramagnetic?

  • (A) (A) O\(_2\)
  • (B) (B) N\(_2^+\)
  • (C) (C) O\(_2^{2-}\)
  • (D) (D) C\(_2\)

Question 124:

Volume of 4.4 g CO\(_2\) at STP is:

  • (A) (A) 22.4 L
  • (B) (B) 2.24 L
  • (C) (C) 11.2 L
  • (D) (D) 44.8 L

Question 125:

Match the following:


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

Question 126:

An ideal gas with density (3.0 ,g L^{-1}) has a pressure of (684 ,mm Hg) at (25^{circ}C). The rms speed (in m s^{-1}) of the gas is (1 ,atm = 10^{5} ,Pa).

  • (A) (A) \(3 10^{2}\)
  • (B) (B) \(3 10^{3}\)
  • (C) (C) \(4 10^{2}\)
  • (D) (D) \(4 10^{3}\)

Question 127:

If the molar masses of Na\(_2\)S\(_2\)O\(_3\) and I\(_2\) are M\(_1\) and M\(_2\) respectively, then the equivalent weights of Na\(_2\)S\(_2\)O\(_3\) and I\(_2\) in the reaction: \[ 2\,Na_2S_2O_3 + I_2 arrow 2\,NaI + Na_2S_4O_6 \]
are respectively:

  • (A) M\(_1\), M\(_2\)
  • (B) M\(_1\), frac{M_2}{2}
  • (C) 2M\(_1\), M\(_2\)
  • (D) frac{M_1}{2}, M\(_2\)

Question 128:

At 27^{circ}C, 1.6 g of O\(_2\) gas at 5 atm expands isothermally against a constant external pressure of 1 atm. The work done (in J) is (1 L-atm = 100 J):

  • (A) -49.2
  • (B) -98.4
  • (C) +98.4
  • (D) +49.2

Question 129:

For the reaction, \(2Al_{2}O_{3}(s) arrow 4Al(s) + 3O_{2}(g)\), \(\Delta H = +3340\,kJ\). What is the enthalpy of formation of \(Al_{2}O_{3}(s)\) (in kJ)?

  • (A) +1670
  • (B) -3340
  • (C) +3340
  • (D) -1670

Question 130:

The minimum volume of water (in L) required to dissolve 1.5 g of \(CaSO_{4}\) (molar mass = 136 g mol\(^{-1}\)) at 298 K is given that \(K_{sp} = 9 10^{-6}\).

  • (A) 6.37
  • (B) 7.37
  • (C) 3.67
  • (D) 3.73

Question 131:

At a given temperature T in a 10.0 L flask, 2.0 moles of N\(_2\)O\(_4\)(g) is heated. At equilibrium, 20% of N\(_2\)O\(_4\)(g) dissociates into NO\(_2\)(g). The value of K\(_C\) for the reaction N\(_2\)O\(_4\)(g) \( leftharpoons\) 2NO\(_2\)(g) is:

  • (A) 2 10^{-2}
  • (B) 4 10^{-2}
  • (C) 3 10^{-2}
  • (D) 6 10^{-2}

Question 132:

Which of the following statements are correct regarding methods used to remove hardness of water?

I. Temporary hardness due to Ca and Mg bicarbonates can be removed by boiling.
II. In Clark's process, lime is used to precipitate calcium carbonate.
III. Calgon softens water by forming soluble complexes with Ca\(^{2+}\) and Mg\(^{2+}\).

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

Question 133:

X, Y, Z are calcium compounds. X is a primary raw material for manufacturing cement. Y is used to recover ammonia in Solvay process and Z is employed for making casts of statues. Identify the incorrect statement from the following:

  • (A) Y is prepared by adding water to X
  • (B) Y is also used as a starting material to manufacture bleaching powder
  • (C) Z is formed by heating gypsum at 373 K
  • (D) X with P\(_4\)O\(_{10}\) forms calcium phosphate

Question 134:

NaBH\(_4\) reacts with I\(_2\) and gives a salt and two gases Y, Z. The gas Y is toxic in nature. Z is a combustible gas. The correct statements regarding Y, Z are:


I. Y with NaH forms a compound which acts as a good reducing agent.
II. Y on hydrolysis gives a monobasic acid.
III. Z is used in Haber’s process.

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

Question 135:

Which of the following compounds is not correctly matched with the property given?

  • (A) Silica - Has high melting point
  • (B) Stannous chloride - good oxidizing agent
  • (C) Silicones - water-repellent and heat-resistant
  • (D) Zeolites - ion-exchangers

Question 136:

The number of lone pairs on the central atom in ( SF_{4} ), ( XeF_{4} ), ( CF_{4} ), and ( BF_{3} ) are respectively:


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

Question 137:

Which of the following transition metal complexes is expected to be diamagnetic?

  • (A) [Ni(CN)\(_4\)]\(^{2-}\)
  • (B) [NiCl\(_4\)]\(^{2-}\)
  • (C) [Fe(H\(_2\)O)\(_6\)]\(^{3+}\)
  • (D) [CoF\(_6\)]\(^{3-}\)

Question 138:

Which of the following elements has the highest first ionization enthalpy?

  • (A) Boron
  • (B) Carbon
  • (C) Nitrogen
  • (D) Oxygen

Question 139:

The IUPAC name of the complex [Pt(NH\(_{3}\))\(_{2}\)Cl(NO\(_{2}\))] is:

  • (A) Diamminochloronitroplatinum(II)
  • (B) Diamminochloronitrito-N-platinum(II)
  • (C) Diamminechloronitrito-N-platinum(II)
  • (D) Diamminechloronitro-N-platinum(II)

Question 140:

The reaction of H\(_2\)O\(_2\) with KIO\(_4\) in an alkaline medium gives:

  • (A) KIO\(_3\) + H\(_2\)O + O\(_2\)
  • (B) KIO\(_3\) + H\(_2\)O + O\(_3\)
  • (C) KI + H\(_2\)O + O\(_2\)
  • (D) KIO\(_3\) + H\(_2\)O + H\(_2\)

Question 141:

The boiling point of 1M aqueous solution of KCl (85% dissociation) having density \(1.04\ g mL^{-1}\) is
\[ (Given: K_b(\mathrm{H_2O}) = 0.52\ \mathrm{K\ kg\ mol^{-1}}, \quad Molar mass of KCl = 74.5\ \mathrm{g\ mol^{-1}} ) \]

  • (A) \(100.096^\circ \mathrm{C}\)
  • (B) \(100.996^\circ \mathrm{C}\)
  • (C) \(100.896^\circ \mathrm{C}\)
  • (D) \(100.796^\circ \mathrm{C}\)

Question 142:

Which of the following statements are correct about a dry cell?


[(I)] It is also known as Leclanche cell.
[(II)] Electrolyte is a moist paste of \(NH_4Cl\) and \(ZnCl_2\).
[(III)] Reaction at cathode is
\[ MnO_2 + NH_4^+ + e^- arrow MnO(OH) + NH_3 \]
[(IV)] It can be charged.


The correct answer is

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

Question 143:

The emf values of three galvanic cells I, II and III are \(E_1\), \(E_2\) and \(E_3\) respectively. Determine the correct order among them.
\[ (I)\quad Zn|Zn^{2+}(1M)||Cu^{2+}(0.1M)|Cu \]
\[ (II)\quad Zn|Zn^{2+}(1M)||Cu^{2+}(1M)|Cu \]
\[ (III)\quad Zn|Zn^{2+}(0.1M)||Cu^{2+}(1M)|Cu \]

  • (A) \(E_3 > E_2 > E_1\)
  • (B) \(E_1 > E_2 > E_3\)
  • (C) \(E_2 > E_3 > E_1\)
  • (D) \(E_1 > E_3 > E_2\)

Question 144:

The value of the rate constant for the reaction \(A arrow products\) is \(5 10^{-5}\ \mathrm{s^{-1}}\) at \(300\ \mathrm{K}\). Its activation energy is \(50\ \mathrm{kJ\ mol^{-1}}\). At temperature \(T\), the rate constant becomes \(1.0 10^{-4}\ \mathrm{s^{-1}}\). What is the value of \(T\) (in K)?
\[ Given: R = 8.3\ \mathrm{J\ mol^{-1}\ K^{-1}}, \qquad \log 2 = 0.3 \]

  • (A) 397
  • (B) 311
  • (C) 286
  • (D) 345

Question 145:

Match List-I with List-II.


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

Question 146:

Given below are two statements:

Statement I: Animal skin is positively charged and tannin is negatively charged.

Statement II: In leather tanning, chromium salts are used in place of tannin.

The correct answer is

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

Question 147:

Consider the following steps involved in the extraction of Aluminium. What is \(Z\)?
\[ Bauxite \xrightarrow[\;523K\;]{Hot conc. NaOH} X(aq) \xrightarrow[\;CO_2\;]{} Y \xrightarrow[\;1473K\;]{} Z \xrightarrow[\;electrolysis\;]{} Al \]

  • (A) \(Al(OH)_3\)
  • (B) \(Al_2(CO_3)_3\)
  • (C) \(Al_2O_3\)
  • (D) \(Al(HCO_3)_3\)

Question 148:

Which halogen oxide is used in the estimation of carbon monoxide?

  • (A) \(Cl_2O_7\)
  • (B) \(BrO_3\)
  • (C) \(I_2O_7\)
  • (D) \(I_2O_5\)

Question 149:

Given below are two statements:

Statement I:
The formation of \([O_2]^+[PtF_6]^-\) is the basis for the formation of xenon fluorides.

Statement II: \(O_2\) and Xe have almost the same first ionization enthalpies.

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 150:

A transition metal ion \(X^{3+}\) has a magnetic moment of \(\sqrt{15}\) BM. The atomic number of the metal \(X\) is

  • (A) 24
  • (B) 25
  • (C) 26
  • (D) 27

Question 151:

The number of complexes among the following having exactly four unpaired electrons is
\[ [Cr(H_2O)_6]^{2+}, \; [Mn(H_2O)_6]^{2+}, \; [Fe(H_2O)_6]^{2+}, \; [Co(H_2O)_6]^{3+}, \]
\[ [Cu(H_2O)_6]^{2+}, \; [CoF_6]^{3-}, \; [Cr(CN)_6]^{4-}, \; [MnCl_4]^{2-} \]

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

Question 152:

Non-stick cookware is coated with Teflon and unbreakable crockery is made up of melamine-formaldehyde resin. The correct classification of these polymers respectively is

  • (A) Addition copolymer ; Condensation homopolymer
  • (B) Addition homopolymer ; Condensation copolymer
  • (C) Condensation homopolymer ; Addition copolymer
  • (D) Condensation copolymer ; Addition homopolymer

Question 153:

Given below are two statements:

Statement I: Sucrose consists of \(\alpha\)-D-glucose and \(\beta\)-D-fructose units.

Statement II: Lactose consists of \(\beta\)-D-galactose and \(\beta\)-D-glucose units.

  • (A) Both Statement I and Statement II are correct.
  • (B) Statement I is correct but Statement II is incorrect.
  • (C) Statement I is incorrect but Statement II is correct.
  • (D) Both Statement I and Statement II are incorrect.

Question 154:

Histamine is responsible for various physiological effects. Which of the following statements are correct?


[(I)] Histamine is a potent vasodilator.
[(II)] Histamine lowers blood pressure by constricting blood vessels.
[(III)] Histamine is responsible for nasal congestion associated with common cold and allergies.

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

Question 155:

Toluene undergoes bromination in presence of iron followed by treatment with sodium in dry ether. The major product formed is
\[ C_6H_5CH_3 \xrightarrow{Br_2/Fe} X \xrightarrow{2Na,\ dry\ ether} Y \]

  • (A) Biphenyl
  • (B) \(p,p'\)-Dimethylbiphenyl
  • (C) Diphenylmethane
  • (D) Ethylbenzene

Question 156:

Among the following amines, the one which will give carbylamine test is

  • (A) Trimethylamine
  • (B) Dimethylamine
  • (C) Aniline
  • (D) Triethylamine

Question 157:

The correct structure of the complex \([Ni(CN)_4]^{2-}\) and its magnetic property are

  • (A) Tetrahedral, Paramagnetic
  • (B) Square planar, Diamagnetic
  • (C) Tetrahedral, Diamagnetic
  • (D) Square planar, Paramagnetic

Question 158:

Which of the following processes represents the extraction of pure metal from its ore?

  • (A) Calcination
  • (B) Roasting
  • (C) Electrolytic Refining
  • (D) Smelting

Question 159:

The correct IUPAC name of the compound
\[ CH_3-CH(CH_3)-CH_2-CH(OH)-CH_3 \]

is:

  • (A) 4-Methylpentan-2-ol
  • (B) 2-Methylpentan-4-ol
  • (C) 2-Methylpentan-2-ol
  • (D) 4-Methylpentan-4-ol

Question 160:

Which of the following coordination compounds exhibits optical isomerism?

  • (A) \([Co(NH_3)_4Cl_2]^+\)
  • (B) \([Co(en)_2Cl_2]^+\)
  • (C) \([Co(NH_3)_5Cl]^{2+}\)
  • (D) \([Co(NH_3)_6]^{3+}\)

AP EAPCET 2026 Paper Pattern – Engineering

Section Number of Questions Marks per Question Weightage Total Marks
Mathematics 80 1 80 80
Physics 40 1 40 40
Chemistry 40 1 40 40
Total 160 1 160 160

AP EAPCET 2026 Engineering Paper Analysis