NDA II 2016 Mathematics

• Question 1
  Let S be the set of all distinct numbers of the form $\frac{\mathit{p}}{\mathit{q}}$ where p, q$\in \left\{1, 2, 3, 4, 5, 6\right\}.$What is the cardinality of the set S?

  Option A: 21

  Option B: 23

  Option C: 32

  Option D: 36

  VIEW SOLUTION

• Question 2
  If c > 0 and 4a + c < 2b, then $a{x}^2-bx+c=0$ has a root in which one of the following intervals?

  Option A: (0, 2)

  Option B: (2, 3)

  Option C: (3, 4)

  Option D: (–2, 0)

  VIEW SOLUTION

• Question 3
   If A = $\left\{x\in \mathit{R}:x^2+6x-7<0\right\}$ and B = $\left\{x\in \mathit{R}:x^2+9x+14>0\right\}$, then which of the following is /are correct?
  (I) $A\cap B=\left\{x\in \mathit{R}:-2<x<1\right\}$
  (II) A\B $\{x\in \mathit{R}:-7<x<-2\}$
  Select the correct answer using the code given below :

  Option A: 1 only

  Option B: 2 only

  Option C: Both 1 and 2

  Option D: Neither 1 nor 2

  VIEW SOLUTION

• Question 4
  If A is a square matrix of order 3 and det A = 5, then what is det $\left[2{\left(\mathrm{A}\right)}^{-1}\right]$ equal to?

  Option A: $\frac{1}{10}$

  Option B: $\frac{2}{5}$

  Option C: $\frac{8}{5}$

  Option D: $\frac{1}{40}$

  VIEW SOLUTION

• Question 5
  What is ${\omega }^{\mathrm{100}}+{\omega }^{\mathrm{200}}+{\omega }^{\mathrm{300}}$ equal to, where ω is the cube root of unity?

  Option A: 1

  Option B: 3ω

  Option C: 3ω²

  VIEW SOLUTION

• Question 6
  If $\mathrm{Re}\left(\frac{z-1}{z+1}\right)=0$ , where z = x + iy is a complex number, then which one of the following is correct?

  Option A: z = 1 + i

  Option B: |z| = 2

  Option C: z = 1 – i

  Option D: |z| = 1

  VIEW SOLUTION

• Question 7
  What is [x y z] $\left[\begin{array}{ccc}\mathit{a}& \mathit{h}& \mathit{g}\\ \mathit{h}& \mathit{b}& \mathit{f}\\ \mathit{g}& \mathit{f}& \mathit{c}\end{array}\right]$ equal to?

  Option A: $\left[\begin{array}{ccc}ax+hy+gz& h+b+f& g+f+c\end{array}\right]$

  Option B: $\left[\begin{array}{ccc}\mathit{a}& \mathit{h}& \mathit{g}\\ \mathit{h}\mathit{x}& \mathit{b}\mathit{y}& \mathit{f}\mathit{z}\\ \mathit{g}& \mathit{f}& \mathit{c}\end{array}\right]$

  Option C: $\left[\begin{array}{l}ax+hy+gz\\ hx+by+fz\\ gx+fy+cz\end{array}\right]$

  Option D: $\left[\begin{array}{ccc}ax+hy+gz& hx+by+fz& gx+fy+cz\end{array}\right]$

  VIEW SOLUTION

• Question 8
  Out of 15 points in a plane, n points are in the same straight line. 445 triangles can be formed by joining these points. What is the value of n?

  Option A: 3

  Option B: 4

  Option C: 5

  Option D: 6

  VIEW SOLUTION

• Question 9
  If ${z=\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)}^{107}+{\left(\frac{\sqrt{3}}{2}-\frac{i}{2}\right)}^{107},$ then what is the imaginary part of z equal to?

  Option B: $\frac{1}{2}$

  Option C: $\frac{\sqrt{3}}{2}$

  Option D: 1

  VIEW SOLUTION

• Question 10
  If both the roots of the equation $x^2-2kx+k^2-4=0$ lie between –3 and 5, then which one of the following is correct?

  Option A: $-2<k<2$

  Option B: $-5<k<3$

  Option C: $-3<k<5$

  Option D: $-1<k<3$

  VIEW SOLUTION

• Question 11
  What is the number of distinct solutions of the equation $z^2+\left|z\right|=0$ (where z is a complex number)?

  Option A: One

  Option B: Two

  Option C: Three

  Option D: Five

  VIEW SOLUTION

• Question 12
  How many geometric progressions is/are possible containing 27, 8 and 12 as three of its/their terms?

  Option A: One

  Option B: Two

  Option C: Four

  Option D: Infinitely many

  VIEW SOLUTION

• Question 13
  Let R be a relation from A = (1, 2, 3, 4) to B = (1, 3, 5) such that R = [(a, b) : a < b, where a ∈ A and b ∈ B].
  What is RoR^–1 equal to?

  Option A: $\left[\left(1, 3\right), \left(1, 5\right), \left(2, 3\right), \left(2, 5\right), \left(3, 5\right), \left(4, 5\right)\right]$

  Option B: $\left[\left(3, 1\right), \left(5, 1\right), \left(3, 2\right), \left(5, 2\right), \left(5, 3\right), \left(5, 4\right)\right]$

  Option C: $\left[\left(3, 3\right), \left(3, 5\right), \left(5, 3\right), \left(5, 5\right)\right]$

  Option D: $\left[\left(3, 3\right), \left(3, 4\right), \left(4, 5\right)\right]$

  VIEW SOLUTION

• Question 14
  A five-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3 and 4 without repetition of digits. What is the number of ways this can be done?

  Option A: 96

  Option B: 48

  Option C: 32

  Option D: No number can be formed

  VIEW SOLUTION

• Question 15
  What is ${}^{47}{C}_4{+}^{51}{C}_3+{\sum _{j=2}^5}^{52-j}{C}_3$ equal to?

  Option A: ${}^{52}{C}_4$

  Option B: ${}^{51}{C}_5$

  Option C: ${}^{53}{C}_4$

  Option D: ${}^{52}{C}_5$

  VIEW SOLUTION

• Question 16
  Let a, x, y, z, b be in AP, where x + y + z = 15. Let a, p, q, r, b be in HP, where $p^{-1}+q^{-1}+r^{-1}=5/3.$
  
  What is the value of ab?

  Option A: 10

  Option B: 9

  Option C: 8

  Option D: 6

  VIEW SOLUTION

• Question 17
  Let a, x, y, z, b be in AP, where x + y + z = 15. Let a, p, q, r, b be in HP, where $p^{-1}+q^{-1}+r^{-1}=5/3.$
  
  What is the value of xyz?

  Option A: 120

  Option B: 105

  Option C: 90

  Option D: Cannot be determined

  VIEW SOLUTION

• Question 18
  Let a, x, y, z, b be in AP, where x + y + z = 15. Let a, p, q, r, b be in HP, where $p^{-1}+q^{-1}+r^{-1}=5/3.$
  
  What is the value of pqr?

  Option A: $\frac{35}{243}$

  Option B: $\frac{81}{35}$

  Option C: $\frac{243}{35}$

  Option D: Cannot be determined

  VIEW SOLUTION

• Question 19
  The sixth term of an AP is 2 and its common difference is greater than 1.
  
  What is the common difference of the AP so that the product of the first, fourth and the fifth terms isthe greatest?

  Option A: 8/5

  Option B: 9/5

  Option C: 2

  Option D: 11/5

  VIEW SOLUTION

• Question 20
  The sixth term of an AP is 2 and its common difference is greater than 1.
  
  What is the first term of the AP, so that the product of the first,fourth and the fifth terms is the greatest?

  Option A:  –4

  Option B: –6

  Option C: –8

  Option D: –10

  VIEW SOLUTION

• Question 21
  $\mathrm{Let}\mathrm{\hspace{0.17em}\hspace{0.17em}}a{x}^3+b{x}^2+cx+d=\left|\begin{array}{l}x+1\\ 2x+3\\ 2-x\end{array}\begin{array}{cc}2x& 3x\\ x+1& x\\ 3x+4& 5x-1\end{array}\right|$, then
  
  What is the value of c?

  Option A: –1

  Option B: 34

  Option C: 35

  Option D: 50

  VIEW SOLUTION

• Question 22
  $\mathrm{Let}\mathrm{\hspace{0.17em}\hspace{0.17em}}a{x}^3+b{x}^2+cx+d=\left|\begin{array}{l}x+1\\ 2x+3\\ 2-x\end{array}\begin{array}{cc}2x& 3x\\ x+1& x\\ 3x+4& 5x-1\end{array}\right|$, then
  
  What is the value of a + b + c + d?

  Option A: 62

  Option B: 63

  Option C: 65

  Option D: 68

  VIEW SOLUTION

• Question 23
  The interior angles of a polygon of n sides are in AP. The smallest angle is 120° and the common difference is 5°.
  
  How many possible values can n have

  Option A: One

  Option B: Two

  Option C: Three

  Option D: Infinitely many

  VIEW SOLUTION

• Question 24
  The interior angles of a polygon of n sides are in AP. The smallest angle is 120° and the common difference is 5°.
  
  What is the largest interior angle of the polygon?

  Option A: 160° only

  Option B: 195° only

  Option C: Either 160° or 195°

  Option D: Neither 160° nor 195°

  VIEW SOLUTION

• Question 25
  If $m=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$  and $n=\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right],$ then what is the value of the determinant of m cosθ – n sinθ?

  Option A: –1

  Option C: 1

  Option D: 2

  VIEW SOLUTION

• Question 26
  If $f\left(x\right)=\left[\begin{array}{ccc}\cos x& -\sin x& 0\\ \sin x& \cos x& 0\\ 0& 0& 1\end{array}\right]$, then which of the following are correct?
  
  1. $f\left(\theta \right)\times f\left(\varphi \right)=f(\theta +\varphi ).$
  2. The value of the determinant of the matrix $f\left(\theta \right)\times f\left(\varphi \right)$ is 1.
  3. The determinant of f(x) is an even function.
  Select the correct answer using the code given below :

  Option A: 1 and 2 only

  Option B: 2 and 3 only

  Option C: 1 and 3 only

  Option D: 1, 2 and 3

  VIEW SOLUTION

• Question 27
  Which of the following are correct in respect of the system of equations x + y + z = 8, x – y + 2z = 6 and 3x – y + 5z = k?
  1. They have no solution, if k = 15.
  2. They have infinitely many solutions, if k = 20.
  3. They have unique solution, if k = 25.
  Select the correct answer using the code given below :

  Option A: 1 and 2 only

  Option B: 2 and 3 only

  Option C: 1 and 3 only

  Option D: 1, 2 and 3

  VIEW SOLUTION

• Question 28
  If $A=\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$ and $B=\left[\begin{array}{cc} 2& 3\\ -1& -2\end{array}\right]$ then which of the following is/are correct?
  
  1. $AB\left(A^{-1}{B}^{-1}\right)$ is a unit matrix.
  2. ${\left(AB\right)}^{-1}=A^{-1}{B}^{-1}.$
  Select the correct answer using the code given below :

  Option A: 1 only

  Option B: 2 only

  Option C: Both 1 and 2

  Option D: Neither 1 nor 2

  VIEW SOLUTION

• Question 29
  If $x^{\mathrm{In}\hspace{0.17em}\left(\frac{y}{z}\right)}\cdot y{\hspace{0.17em}}^{\mathrm{In}\mathrm{\hspace{0.17em}\hspace{0.17em}}{\left(x\hspace{0.17em}z\right)}^2}\cdot z^{\mathrm{In}\hspace{0.17em}\left(\frac{x}{y}\right)}=y{\hspace{0.17em}}^{\mathrm{4\hspace{0.17em}}\hspace{0.17em}\mathrm{In}\mathrm{\hspace{0.17em}\hspace{0.17em}}y}$ for any x >1, y > 1 and z > 1, then which one of the following is correct?

  Option A: ln y is the GM of ln x, ln x, ln x and ln z

  Option B: ln y is the AM of ln x, ln x, ln x and ln z

  Option C: ln y is the HM of ln x, ln x, ln x and ln z

  Option D: ln y is the AM of ln x, ln x, ln z and ln z

  VIEW SOLUTION

• Question 30
  If the number 235 in the decimal system is converted into the binary system, then what is the resulting number?

  Option A: (11110011)₂

  Option B: (11101011)₂

  Option C: (11110101)₂

  Option D: (11011011)₂

  VIEW SOLUTION

• Question 31
  Let α and β be the roots of the equation
  
  $x^2-(1-2a^2)x+(1-2a^2)=0$.
  
  Under what condition, does the above equation have real roots?

  Option A: $a^2<\frac{1}{2}$

  Option B: $a^2>\frac{1}{2}$

  Option C: $a^2\le \frac{1}{2}$

  Option D: $a^2\ge \frac{1}{2}$

  VIEW SOLUTION

• Question 32
  Let α and β be the roots of the equation
  
  $x^2-(1-2a^2)x+(1-2a^2)=0$.
  
  Under what condition is $\frac{1}{{\alpha }^2}+\frac{1}{{\beta }^2}<1?$

  Option A: $a^2<\frac{1}{2}$

  Option B: $a^2>\frac{1}{2}$

  Option C: $a^2>1$

  Option D: $a^2\in \left(\frac{1}{3},\frac{1}{2}\right)$ only

  VIEW SOLUTION

• Question 33
  What is $\sqrt{\frac{1+{\omega }^2}{1+\omega }}$ equal to, where ω is the cube root of unity?

  Option A: 1

  Option B: ω

  Option C: ω²

  Option D: $i\mathrm{\omega }, \mathrm{where} i=\sqrt{-1}$

  VIEW SOLUTION

• Question 34
  In an examination, 70% students passed in Physics, 80% students passed in Chemistry, 75% students passed in Mathematics and 85% students passed in Biology, and x% students failed in all the four subjects. What is the minimum value of x?

  Option A: 10

  Option B: 12

  Option C: 15

  Option D: None of the above

  VIEW SOLUTION

• Question 35
  For the system of linear equations, 2x + 3y + 5z = 9, 7x + 3y – 2z = 8 and 2x + 3y + λz = µ
  
  Under what condition, does the above system of equations have infinitely many solutions?

  Option A: λ = 5 and µ ≠ 9

  Option B: λ = 5 and µ = 9

  Option C: λ = 9 and µ = 5

  Option D: λ = 9 and µ ≠ 5

  VIEW SOLUTION

• Question 36
  For the system of linear equations, 2x + 3y + 5z = 9, 7x + 3y – 2z = 8 and 2x + 3y + λz = µ
  
  Under what condition, does the above system of equations have unique solutions?

  Option A: λ = 5 and µ = 9

  Option B: λ ≠ 5 and µ = 7 only

  Option C: λ ≠ 5 and µ has any real value

  Option D: λ has any real value and µ ≠ 9

  VIEW SOLUTION

• Question 37
  What is the number of odd integers between 1000 and 9999 with no digit repeated?

  Option A: 2100

  Option B: 2120

  Option C: 2240

  Option D: 3331

  VIEW SOLUTION

• Question 38
  What is the greatest value of the positive integer n satisfying the condition $1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2^{n-1}}<2-\frac{1}{1000}$?

  Option A: 8

  Option B: 9

  Option C: 10

  Option D: 11

  VIEW SOLUTION

• Question 39
  $2x^2+3x-\alpha =0$ has roots –2 and β while the equation $x^2-3mx+2m^2=0$ has both the roots positive, where α > 0 and β > 0.
  
  What is the value of α?

  Option A: 1/2

  Option B: 1

  Option C: 2

  Option D: 4

  VIEW SOLUTION

• Question 40
  $2x^2+3x-\alpha =0$ has roots –2 and β while the equation $x^2-3mx+2m^2=0$ has both the roots positive, where α > 0 and β > 0.
  
  If β, 2, 2m is in GP, then what is the value of $\beta \sqrt{m}$?

  Option A: 1

  Option B: 2

  Option C: 4

  Option D: 6

  VIEW SOLUTION

• Question 41
  Sin A + 2 sin 2A + sin 3A is equal to which of the following?
  
  1. $4 \sin 2\mathrm{A} {\cos }^2\left(\frac{\mathrm{A}}{2}\right)$
  
  2. $2 \sin 2\mathrm{A} {\left(\sin \frac{\mathrm{A}}{2}+\cos \frac{\mathrm{A}}{2}\right)}^2$
  3. $8 \sin \mathrm{A} \cos \mathrm{A} {\cos }^2 \left(\frac{\mathrm{A}}{2}\right)$
  Select the correct answer using the code given below:

  Option A: 1 and 2 only

  Option B: 2 and 3 only

  Option C: 1 and 3 only

  Option D: 1, 2 and 3

  VIEW SOLUTION

• Question 42
  If x = sin 70° · sin 50° and y = cos 60° · cos 80°, then what is xy equal to?

  Option A: 1/16

  Option B: 1/8

  Option C: 1/4

  Option D: 1/2

  VIEW SOLUTION

• Question 43
  If $\sin {\theta }_1+\sin {\theta }_2+\sin {\theta }_3+\sin {\theta }_4=4,$ then what is the value of $\cos {\theta }_1+\cos {\theta }_2+\cos {\theta }_3+\cos {\theta }_4?$

  Option B: 1

  Option C: 2

  Option D: 4

  VIEW SOLUTION

• Question 44
  What is the value of $\left(1+\cos \frac{\pi }{8}\right) \left(1+\cos \frac{3\pi }{8}\right) \left(1+\cos \frac{5\pi }{8}\right) \left(1+\cos \frac{7\pi }{8}\right)?$

  Option A: $\frac{1}{2}$

  Option B: $\frac{1}{2}+\frac{1}{2\sqrt{2}}$

  Option C: $\frac{1}{2}-\frac{1}{2\sqrt{2}}$

  Option D: $\frac{1}{8}$

  VIEW SOLUTION

• Question 45
  If $x \cos \theta +y \sin \theta =z$ , then what is the value of ${\left(x \sin \theta -y \cos \theta \right)}^2?$

  Option A: $x^2+y^2-z^2$

  Option B: $x^2-y^2-z^2$

  Option C: $x^2-y^2+z^2$

  Option D: $x^2+y^2+z^2$

  VIEW SOLUTION

• Question 46
  What is the value of cos $\left(2{\cos }^{-1} 0.8\right)?$

  Option A: 0.81

  Option B: 0.56

  Option C: 0.48

  Option D: 0.28

  VIEW SOLUTION

• Question 47
  The top of a hill when observed from the top and bottom of a building of height h is at angles of elevation p and q, respectively. What is the height of the hill?

  Option A: $\frac{h \cot q}{\cot q-\cot p}$

  Option B: $\frac{h \cot p}{\cot p-\cot q}$

  Option C: $\frac{2h \tan p}{\tan p-\tan q}$

  Option D: $\frac{2h \tan q}{\tan q-\tan p}$

  VIEW SOLUTION

• Question 48
  If $\sin 18°=\frac{\sqrt{5}-1}{4},$ then what is the value of sin 81°?

  Option A: $\frac{\sqrt{3+\sqrt{5}}+\sqrt{5-\sqrt{5}}}{4}$

  Option B: $\frac{\sqrt{3+\sqrt{5}}+\sqrt{5+\sqrt{5}}}{4}$

  Option C: $\frac{\sqrt{3-\sqrt{5}}+\sqrt{5-\sqrt{5}}}{4}$

  Option D: $\frac{\sqrt{3+\sqrt{5}}-\sqrt{5-\sqrt{5}}}{4}$

  VIEW SOLUTION

• Question 49
  A moving boat is observed from the top of a cliff of 150 m height. The angle of depression of the boat changes from 60° to 45° in 2 minutes. What is the speed of the boat in meter per hour?

  Option A: $\frac{4500}{\sqrt{3}}$

  Option B: $\frac{4500\left(\sqrt{3}-1\right)}{\sqrt{3}}$

  Option C: $4500\sqrt{3}$

  Option D: $\frac{4500\left(\sqrt{3}+1\right)}{\sqrt{3}}$

  VIEW SOLUTION

• Question 50
  What is $\frac{1-\tan 2°\cot 62°}{\tan 152°-\cot 88°}$ equal to?

  Option A: $\sqrt{3}$

  Option B: $-\sqrt{3}$

  Option C: $\sqrt{2}-1$

  Option D: $1-\sqrt{2}$

  VIEW SOLUTION

• Question 51
  An equilateral triangle has one vertex at (0, 0) and another at $(3,\sqrt{3}).$ What are the coordinates of the third vertex?

  Option A: $\left(0, 2\sqrt{3}\right)$ Only

  Option B: $\left(3,-\sqrt{3}\right)$ Only

  Option C: $\left(0, 2\sqrt{3}\right) \mathrm{or} \left(3,-\sqrt{3}\right)$

  Option D: Neither $\left(0, 2\sqrt{3}\right)$ nor $\left(3,-\sqrt{3}\right)$

  VIEW SOLUTION

• Question 52
  What is the equation of the right bisector of the line segment joining (1, 1) and (2, 3)?

  Option A: $2x+4y-11=0$

  Option B: $2x-4y-5=0$

  Option C: $2x-4y-11=0$

  Option D: $x-y+1=0$

  VIEW SOLUTION

• Question 53
  What is the radius of the circle passing through the point (2, 4) and having centre at the intersection of the lines $x-y=4$ and $2x+3y+7=0?$

  Option A: 3 units

  Option B: 5 units

  Option C: $3\sqrt{3}$ units

  Option D: $5\sqrt{2}$ units

  VIEW SOLUTION

• Question 54
  What is the equation of the hyperbola having latus rectum and eccentricity 8 and $\frac{3}{\sqrt{5}}$ respectively?

  Option A: $\frac{x^2}{25}-\frac{y^2}{20}=1$

  Option B: $\frac{x^2}{40}-\frac{y^2}{20}=1$

  Option C: $\frac{x^2}{40}-\frac{y^2}{30}=1$

  Option D: $\frac{x^2}{30}-\frac{y^2}{25}=1$

  VIEW SOLUTION

• Question 55
  If the point (a, a) lies between the lines $|x+y|=2$, then which one of the following is correct?

  Option A: $\left|a\right|<2$

  Option B: $\left|a\right|<\sqrt{2}$

  Option C: $\left|a\right|<1$

  Option D: $\left|a\right|<\frac{1}{\sqrt{2}}$

  VIEW SOLUTION

• Question 56
  What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x + 4y = 10?

  Option A: 4x + 3y + 2 = 0

  Option B: 4x – y + 2 = 0

  Option C: 4x – 3y – 2 = 0

  Option D: 4x – 3y + 2 = 0

  VIEW SOLUTION

• Question 57
  If (a, b) is at unit distance from the line 8x + 6y + 1 = 0, then which of the following conditions are correct?
  1. 3a – 4b – 4 = 0
  2. 8a + 6b + 11 = 0
  3. 8a + 6b – 9 = 0
  Select the correct answer using the code given below :

  Option A: 1 and 2 only

  Option B: 2 and 3 only

  Option C: 1 and 3 only

  Option D: 1, 2 and 3

  VIEW SOLUTION

• Question 58
  If the ellipse $9x^2+16y^2=144$ intercepts the line 3x + 4y = 12, then what is the length of the chord so formed?

  Option A: 5 units

  Option B: 6 units

  Option C: 8 units

  Option D: 10 units

  VIEW SOLUTION

• Question 59
  A straight line cuts off an intercept of 2 units on the positive direction of x-axis and passes through the point (–3, 5). What is the foot of the perpendicular drawn from the point (3, 3) on this line?

  Option A: (1, 3)

  Option B: (2, 0)

  Option C: (0, 2)

  Option D: (1, 1)

  VIEW SOLUTION

• Question 60
  What is the eccentricity of rectangular hyperbola?

  Option A: $\sqrt{2}$

  Option B: $\sqrt{3}$

  Option C: $\sqrt{5}$

  Option D: $\sqrt{6}$

  VIEW SOLUTION

• Question 61
  Let Q be the image of the point P (–2, 1, –5) in the plane 3x – 2y + 2z + 1 = 0.
  
  Consider the following :
  1. The coordinates of Q are (4, –3,–1).
  2. PQ is of length more than 8 units.
  3. The point (1, –1, –3) is the mid-point of the line segment PQ and lies on the given plane.
  Which of the above statements are correct?

  Option A: 1 and 2 only

  Option B: 2 and 3 only

  Option C: 1 and 3 only

  Option D: 1, 2 and 3

  VIEW SOLUTION

• Question 62
  Let Q be the image of the point P (–2, 1, –5) in the plane 3x – 2y + 2z + 1 = 0.
  
  Consider the following :
  1. The direction ratios of the line segment PQ are < 3, –2, 2 >.
  2. The sum of the squares of direction cosines of the line segment PQ is unity.
  Which of the above statements is/are correct?

  Option A: 1 only

  Option B: 2 only

  Option C: Both 1 and 2

  Option D: Neither 1 nor 2

  VIEW SOLUTION

• Question 63
  A line L passes through the point P(5, –6, 7) and is parallel to the planes x + y + z = 1 and 2x – y – 2z = 3.
  
  What are the direction ratios of the line of intersection of the given planes?

  Option A: < 1, 4, 3 >

  Option B: < –1, –4, 3 >

  Option C: < 1, –4, 3 >

  Option D: < 1, –4, –3 >

  VIEW SOLUTION

• Question 64
  A line L passes through the point P(5, –6, 7) and is parallel to the planes x + y + z = 1 and 2x – y – 2z = 3.
  
  What is the equation of the line L?

  Option A: $\frac{x-5}{-1}=\frac{y+6}{4}=\frac{z-7}{-3}$

  Option B: $\frac{x+5}{-1}=\frac{y-6}{4}=\frac{z+7}{-3}$

  Option C: $\frac{x-5}{-1}=\frac{y+6}{-4}=\frac{z-7}{3}$

  Option D: $\frac{x-5}{-1}=\frac{y+6}{-4}=\frac{z-7}{-3}$

  VIEW SOLUTION

• Question 65
  Let $\overrightarrow{a}=\hat{i}+\hat{j}, \overrightarrow{b}=3\hat{i}+4\hat{k}$ and $\overrightarrow{b}=\overrightarrow{c}+\overrightarrow{d}$, where $\overrightarrow{c}$ is parallel to $\overrightarrow{a}$ and $\overrightarrow{d}$ is perpendicular to $\overrightarrow{a}$.
  
  What is $\overrightarrow{c}$ equal to?

  Option A: $\frac{3 \left(\hat{i}+\hat{j}\right)}{2}$

  Option B: $\frac{2\left(\hat{i}+\hat{j}\right)}{3}$

  Option C: $\frac{\left(\hat{i}+\hat{j}\right)}{2}$

  Option D: $\frac{\left(\hat{i}+\hat{j}\right)}{3}$

  VIEW SOLUTION

• Question 66
  Let $\overrightarrow{a}=\hat{i}+\hat{j}, \overrightarrow{b}=3\hat{i}+4\hat{k}$ and $\overrightarrow{b}=\overrightarrow{c}+\overrightarrow{d}$, where $\overrightarrow{c}$ is parallel to $\overrightarrow{a}$ and $\overrightarrow{d}$ is perpendicular to $\overrightarrow{a}$.
  
  If $\overrightarrow{d}=x\hat{i}+y\hat{j}+z\hat{k}$ then which of the following equations is/are correct?
  
  1. y – x = 4
  
  2. 2z – 3 = 0
  
  Select the correct answer using the code given below :

  Option A: 1 only

  Option B: 2 only

  Option C: Both 1 and 2

  Option D: Neither 1 nor 2

  VIEW SOLUTION

• Question 67
  Let $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$ be three vectors such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$, and $\overrightarrow{\left|a\right|}=10, \left|\overrightarrow{b}\right|=6$ and $\left|\overrightarrow{c}\right|=14$.
  
  What is $\overrightarrow{a}·\overrightarrow{b}+\overrightarrow{b}·\overrightarrow{c}=+\overrightarrow{c}·\overrightarrow{a}$ equal to?

  Option A: –332

  Option B: –166

  Option D: 166

  VIEW SOLUTION

• Question 68
  Let $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$ be three vectors such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$, and $\overrightarrow{\left|a\right|}=10, \left|\overrightarrow{b}\right|=6$ and $\left|\overrightarrow{c}\right|=14$.
  
  What is the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ ?

  Option A: 30°

  Option B: 45°

  Option C: 60°

  Option D: 75°

  VIEW SOLUTION

• Question 69
  In a right-angled triangle ABC, if the hypotenuse AB = p, then what is $\overrightarrow{\mathrm{AB}}·\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{BC}}·\overrightarrow{\mathrm{BA}}+\overrightarrow{\mathrm{CA}}· \overrightarrow{\mathrm{CB}}$ equal to?

  Option A: p

  Option B: p²

  Option C: 2p²

  Option D: $\frac{p^2}{2}$

  VIEW SOLUTION

• Question 70
  A force $\overrightarrow{F}=3\hat{i}+2\hat{j}-4\hat{k}$ is applied at the point (1, –1, 2). What is the moment of the force about the point (2, –1, 3)?

  Option A: $\hat{i}+4\hat{j}+4\hat{k}$

  Option B: $2\hat{i}+\hat{j}+2\hat{k}$

  Option C: $2\hat{i}-7\hat{j}-2\hat{k}$

  Option D: $2\hat{i}+4\hat{j}-\hat{k}$

  VIEW SOLUTION

• Question 71
  What is the domain of the function $f\left(x\right)=\frac{1}{\sqrt{\left|x\right|-x}}?$

  Option A: (–∞, 0)

  Option B: (0, ∞)

  Option C: 0 < x < 1

  Option D: x > 1

  VIEW SOLUTION

• Question 72
  Consider the following in respect of the function $f\left(x\right)=\left\{\begin{array}{cl}2+x,& x\ge 0\\ 2-x,& x<0\end{array}\right.$
  1.  $\underset{x\to 1}{\lim }f\left(x\right)$ does not exist.
  
  2.  f(x) is differentiable at x = 0.
  
  3. f(x) is continuous at x = 0.
  
  Which of the above statement is/are correct?

  Option A: 1 only

  Option B: 3 only

  Option C: 2 and 3 only

  Option D: 1 and 3 only

  VIEW SOLUTION

• Question 73
  Let f : A → R where  A = R\[0] is such that $f\left(x\right)=\frac{x+\left|x\right|}{x}$. On which one of the following sets is f(x) continuous?

  Option A: A

  Option B: B = {x ∈ R : x ≥ 0}

  Option C: C = {x ∈ R : x ≤ 0}

  Option D: D = R

  VIEW SOLUTION

• Question 74
  Which one of the following statements is correct with respect to the function $f\left(x\right)=x^3 \sin x?$

  Option A: It has local maximum at x = 0.

  Option B: It has local minimum at x = 0.

  Option C: It has neither maximum nor minimum at x = 0.

  Option D: It has maximum value 1.

  VIEW SOLUTION

• Question 75
  What is the area bounded by the curves $\left|y\right|=1-x^2?$  

  Option A: 4/3 square units

  Option B: 8/3 square units

  Option C: 4 square units

  Option D: 16/3 square units

  VIEW SOLUTION

• Question 76
  $f\left(x\right)=\left\{\begin{array}{lr}3x^2+12x-1,& -1\le x\le 2\\ 37-x,& 2<x\le 3\end{array}\right.$
  
  Which of the following statements is /are correct?
  1. f(x) is increasing in the interval [–1, 2].
  2. f(x) is decreasing in the interval (2, 3].
  Select the correct answer using the code given below :

  Option A: 1 only

  Option B: 2 only

  Option C: Both 1 and 2

  Option D: Neither 1 nor 2

  VIEW SOLUTION

• Question 77
  $f\left(x\right)=\left\{\begin{array}{lr}3x^2+12x-1,& -1\le x\le 2\\ 37-x,& 2<x\le 3\end{array}\right.$
  
  Which of the following statements are correct?
  1.  f(x) is continuous at, x = 2.
  2.  f(x) attains greatest value at x = 2.
  3.  f(x) is differentiable at x = 2.
  Select the correct answer using the code given below :

  Option A: 1 and 2 only

  Option B: 2 and 3 only

  Option C: 1 and 3 only

  Option D: 1, 2 and 3

  VIEW SOLUTION

• Question 78
  Let $f\left(x\right)={\left[\left|x\right|-\left|x-1\right|\right]}^2$.
  
  What is f’(x) equal to when x >1?

  Option B: 2x – 1

  Option C: 4x – 2

  Option D: 8x – 4

  VIEW SOLUTION

• Question 79
  Let $f\left(x\right)={\left[\left|x\right|-\left|x-1\right|\right]}^2$.
  
  What is f’(x) equal to when 0 < x < 1?

  Option B: 2x – 1

  Option C: 4x –2

  Option D: 8x – 4

  VIEW SOLUTION

• Question 80
  Let $f\left(x\right)={\left[\left|x\right|-\left|x-1\right|\right]}^2$.
  
  Which of the following equations is/are correct?
  1. f(–2) = f(5)
  2. f” (–2) + f” (0·5) + f” (3) = 4
  Select the correct answer using the code given below :

  Option A: 1 only

  Option B: 2 only

  Option C: Both 1 and 2

  Option D: Neither 1 nor 2

  VIEW SOLUTION

• Question 81
  Let f(x) = [x], where [·] is the greatest integer function and g(x) = sin x be two real valued functions over ℝ.
  
  Which of the following statements is correct?

  Option A: Both f(x) and g(x) are continuous at x = 0.

  Option B: f(x) is continuous at x = 0 but g(x) is not continuous at x = 0.

  Option C: g(x) is continuous at x = 0 but f(x) is not continuous at x = 0.

  Option D: Both f(x) and g(x) are discontinuous at x = 0.

  VIEW SOLUTION

• Question 82
  Let f(x) = [x], where [·] is the greatest integer function and g(x) = sin x be two real valued functions over ℝ.
  
  Which one of the following statements is correct?

  Option A: $\underset{x\to 0}{\lim }\left(fog\right)\left(x\right)\mathrm{exists}.$

  Option B: $\underset{x\to 0}{\lim }\left(gof\right)\left(x\right)\mathrm{exists}.$

  Option C: $\underset{x\to 0^{-}}{\lim }\left(fog\right)\left(x\right)=\underset{x\to 0^{-}}{\lim }\left(gof\right)\left(x\right)$

  Option D: $\underset{x\to 0^{-}}{\lim }\left(fog\right)\left(x\right)=\underset{x\to 0^{+}}{\lim }\left(gof\right)\left(x\right)$

  VIEW SOLUTION

• Question 83
  Let f(x) = [x], where [·] is the greatest integer function and g(x) = sin x be two real valued functions over ℝ.
  
  Which of the following statements are correct?
  1. (fof) (x) = f(x).
  2. (gog) (x) = g(x) only when x = 0.
  3. (go(fog))(x) can take only three values.
  Select the correct answer using the code given below.

  Option A: 1 and 2 only

  Option B: 2 and 3 only

  Option C: 1 and 3 only

  Option D: 1, 2 and 3

  VIEW SOLUTION

• Question 84
  Let $f\left(x\right)=\left\{\begin{array}{cc}\frac{e^x-1}{x},& x>0\\ 0,& x=0\end{array}\right.$be a real valued function.
  Which one of the following statements is correct?

  Option A: f(x) is a strictly decreasing function in (0, x).

  Option B: f(x) is a strictly increasing function in (0, x).

  Option C: f(x) is neither increasing nor decreasing in (0, x).

  Option D: f(x) is not decreasing in (0, x).

  VIEW SOLUTION

• Question 85
  Let $f\left(x\right)=\left\{\begin{array}{cc}\frac{e^x-1}{x},& x>0\\ 0,& x=0\end{array}\right.$be a real valued function.
  
  Which of the following statements is/are correct?
  1.  f(x) is right continuous at x = 0.
  2. f(x) is discontinuous at x = 1.
  Select the correct answer using the code given below.

  Option A: 1 only

  Option B: 2 only

  Option C: Both 1 and 2

  Option D: Neither 1 nor 2

  VIEW SOLUTION

• Question 86
  Consider the parabola $y=x^2+7x+2$ and the straight line y = 3x – 3.
  
  What are the coordinates of the point on the parabola which is closest to the straight line?

  Option A: (0, 2)

  Option B: (–2, –8)

  Option C: (–7, 2)

  Option D: (1, 10)

  VIEW SOLUTION

• Question 87
  Consider the parabola $y=x^2+7x+2$ and the straight line y = 3x – 3.
  
  What is the shortest distance from the above point on the parabola to the line?

  Option A: $\frac{\sqrt{10}}{2}$

  Option B: $\frac{\sqrt{10}}{5}$

  Option C: $\frac{1}{\sqrt{10}}$

  Option D: $\frac{\sqrt{5}}{4}$

  VIEW SOLUTION

• Question 88
  Let $f\left(x\right)=\left\{\begin{array}{cc}-2,& -3\le x\le 0\\ x-2,& 0<x\le 3\end{array}\right.$ and $g\left(x\right)=f\left(\left|x\right|\right)+\left|f\left(x\right)\right|$
  
  Which of the following statements is/are correct?
  1. g(x) is differentiable at x = 0.
  2. g(x) is differentiable at x = 2.
  Select the correct answer using the code given below :

  Option A: 1 only

  Option B: 2 only

  Option C: Both 1 and 2

  Option D: Neither 1 nor 2

  VIEW SOLUTION

• Question 89
  Let $f\left(x\right)=\left\{\begin{array}{cc}-2,& -3\le x\le 0\\ x-2,& 0<x\le 3\end{array}\right.$ and $g\left(x\right)=f\left(\left|x\right|\right)+\left|f\left(x\right)\right|$
  
  What is the value of the differential coefficient of g(x) at x = –2?

  Option A: –1

  Option C: 1

  Option D: 2

  VIEW SOLUTION

• Question 90
  Let $f\left(x\right)=\left\{\begin{array}{cc}-2,& -3\le x\le 0\\ x-2,& 0<x\le 3\end{array}\right.$ and $g\left(x\right)=f\left(\left|x\right|\right)+\left|f\left(x\right)\right|$
  
  Which of the following statements are correct?
  1. g(x) is continuous at x = 0.
  2. g(x) is continuous at x = 2.
  3. g(x) is continuous at x = –1.
  Select the correct answer using the code given below :

  Option A: 1 and 2 only

  Option B: 2 and 3 only

  Option C: 1 and 3 only

  Option D: 1, 2 and 3

  VIEW SOLUTION

• Question 91
  Let f(x) be a function such that $f\text{'}\left(\frac{1}{x}\right)+x^3 f\text{'}\left(x\right)=0.$ What is ${\int }_{-1}^{1}f\left(x\right) dx$ equal to?

  Option A: 2f(1)

  Option C: 2f (–1)

  Option D: 4 f(1)

  VIEW SOLUTION

• Question 92
  What is$\int \frac{x^4-1}{x^2\sqrt{x^4+x^2+1}}dx$ equal to?

  Option A: $\sqrt{\frac{x^4+x^2+1}{x}}+C$

  Option B: $\sqrt{x^4+2-\frac{1}{x^2}}+C$

  Option C: $\sqrt{x^2+\frac{1}{x^2}+1}+C$

  Option D: $\sqrt{\frac{x^4-x^2+1}{x}}+C$

  VIEW SOLUTION

• Question 93
  What is the degree and order, respectively, of the differential equation satisfying $e^{y\sqrt{1-x^2}+x\sqrt{1-y^2}}=c{e}^x,$ $\left(\mathrm{where} c>0,\left|x\right|<1,\left|y\right|<1\right)?$

  Option A: 1, 1

  Option B: 1, 2

  Option C: 2, 1

  Option D: 2, 2

  VIEW SOLUTION

• Question 94
  What is the curve that passes through the point (1, 1) and whose slope is $\frac{2y}{x}?$

  Option A: Circle

  Option B: Parabola

  Option C: Ellipse

  Option D: Hyperbola

  VIEW SOLUTION

• Question 95
  If xdy = ydx + y²dy, y > 0 and y (1) = 1, then what is y (–3) equal to?

  Option A: 3 only

  Option B: –1 only

  Option C: Both –1 and 3

  Option D: Neither –1 nor 3

  VIEW SOLUTION

• Question 96
  What is the order of the differential equation $\frac{dx}{dy}+\int y dx=x^3?$

  Option A: 1

  Option B: 2

  Option C: 3

  Option D: Cannot be determined

  VIEW SOLUTION

• Question 97
  Which one of the following differential equations represents the family of straight lines, which are at unit distance from the origin?

  Option A: ${\left(y-x\frac{dy}{dx}\right)}^2=1-{\left(\frac{dy}{dx}\right)}^2$

  Option B: ${\left(y+x\frac{dy}{dx}\right)}^2=1+{\left(\frac{dy}{dx}\right)}^2$

  Option C: ${\left(y-x\frac{dy}{dx}\right)}^2=1+{\left(\frac{dy}{dx}\right)}^2$

  Option D: ${\left(y+x\frac{dy}{dx}\right)}^2=1-{\left(\frac{dy}{dx}\right)}^2$

  VIEW SOLUTION

• Question 98
  What is $\int e^{\sin x}\frac{x{\cos }^{3}x-\sin x}{{\cos }^{2}x}dx$ equal to?

  Option A: $(x+\sec x)e^{\sin x}+C$

  Option B: $(x-\sec x)e^{\sin x}+C$

  Option C: $(x+\tan x)e^{\sin x}+C$

  Option D: $(x-\tan x)e^{\sin x}+C$

  VIEW SOLUTION

• Question 99
  If ${\int }_0^{\pi /2}\frac{dx}{3 \cos x+5}=k {\cot }^{-1}2$, then what is the value of k?

  Option A: 1/4

  Option B: 1/2

  Option C: 1

  Option D: 2

  VIEW SOLUTION

• Question 100
  What is ${\int }_1^3\left|1-x^4\right|dx$ equal to?

  Option A: –232/5

  Option B: –116/5

  Option C: 116/5

  Option D: 232/5

  VIEW SOLUTION

• Question 101
  A special dice with numbers 1, –1, 2, –2, 0 and 3 is thrown thrice. What is the probability that the sum of the numbers occurring on the upper face is zero?

  Option A: 1/72

  Option B: 1/8

  Option C: 7/72

  Option D: 25/216

  VIEW SOLUTION

• Question 102
  There is 25% chance that it rains on any particular day. What is the probability that there is at least one rainy day within a period of 7 days?

  Option A: $1-{\left(\frac{1}{4}\right)}^7$

  Option B: ${\left(\frac{1}{4}\right)}^7$

  Option C: ${\left(\frac{3}{4}\right)}^7$

  Option D: $1-{\left(\frac{3}{4}\right)}^7$

  VIEW SOLUTION

• Question 103
  A salesman has a 70% chance to sell a product to any customer. The behaviour of successive customers is independent. If two customers A and B enter, what is the probability that the salesman will sell the product to customer A or B?

  Option A: 0.98

  Option B: 0.91

  Option C: 0.70

  Option D: 0.49

  VIEW SOLUTION

• Question 104
   A student appears for tests I, II and III. The student is considered successful if he passes in tests I, II or I, III or all the three. The probabilities of the student passing in tests I, II and III are m, n and 1/2 respectively. If the probability of the student to be successful is 1/2, then which one of the following is correct?

  Option A: m (1 + n) = 1

  Option B: n (1 + m) = 1

  Option C: m = 1

  Option D: mn = 1

  VIEW SOLUTION

• Question 105
  Three candidates solve a question. Odds in favour of the correct answer are 5 : 2, 4 : 3 and 3 : 4 respectively for three candidates. What is the probability that at least two of them solve the question correctly?

  Option A: 134/343

  Option B: 149/343

  Option C: 60/343

  Option D: 209/343

  VIEW SOLUTION

• Question 106
  Consider the following statements :
  1. The mean and median are equal in symmetric distribution.
  2. The range is the difference between the maximum value and the minimum value in the data.
  3. The sum of the areas of the rectangles in the histogram is equal to the total area bounded by the frequency polygon and the horizontal axis.
  Which of the above statements are correct?

  Option A: 1 and 2 only

  Option B: 2 and 3 only

  Option C: 1 and 3 only

  Option D: 1, 2 and 3

  VIEW SOLUTION

• Question 107
  The scores of 15 students in an examination were recorded as 10, 5, 8, 16, 18, 20, 8, 10, 16, 20, 18, 11, 16, 14 and 12. After calculating the mean, median and mode, an error is found. One of the values is wrongly written as 16 instead of 18. Which of the following measures of central tendency will change?

  Option A: Mean and median

  Option B: Median and mode

  Option C: Mode only

  Option D: Mean and mode

  VIEW SOLUTION

• Question 108
  For 10 observations on price (x) and supply (y), the following data was obtained :
  
  $\sum x=130, \sum y=220, \sum x^2=2288, \sum y^2=5506$ and $\sum xy=3467.$
  
  What is the line of regression of y on x?

  Option A: y = 0.91x + 8.74

  Option B: y = 1.02x + 8.74

  Option C: y = 1.02x – 7.02

  Option D: y = 0.91x – 7.02

  VIEW SOLUTION

• Question 109
  In a study of two groups, the following results were obtained :
   

  	Group A	Group B
  Sample size	20	25
  Sample mean	22	23
  Sample standard deviation	10	12

  
  Which of the following statements is correct?

  Option A: Group A is less variable than Group B because Group A’s standard deviation is smaller.

  Option B: Group A is less variable than Group B because Group A’s sample size is smaller.

  Option C: Group A is less variable than Group B because Group A’s sample mean is smaller.

  Option D: Group A is less variable than Group B because Group A’s coefficient of variation is smaller.

  VIEW SOLUTION

• Question 110
  Consider the following statements with respect to the class intervals of grouped frequency distribution.
  1. Class-intervals need not be mutually exclusive
  2. Class-intervals should be exhaustive
  3. Class-intervals need not be of equal width
  Which of the above statements are correct?

  Option A: 1 and 2 only

  Option B: 2 and 3 only

  Option C: 1 and 3 only

  Option D: 1, 2 and 3

  VIEW SOLUTION

• Question 111
  A medicine is known to be 75% effective to cure a patient. If the medicine is given to 5 patients, what is the probability that at least one patient is cured by this medicine?

  Option A: $\frac{1}{1024}$

  Option B: $\frac{243}{1024}$

  Option C: $\frac{1023}{1024}$

  Option D: $\frac{781}{1024}$

  VIEW SOLUTION

• Question 112
  For two events A and B, it is given that P(A) = $\frac{3}{5},$ P(B) = $\frac{3}{10}$ and $\mathrm{P}\left(\mathrm{A}\left|\mathrm{B}\right.\right)=\frac{2}{3}$. If $\overline{\mathrm{A}}$ and $\overline{\mathrm{B}}$ are the complementary events of A and B , then what is $\mathrm{P}\left(\overline{\mathrm{A}}\left|\overline{\mathrm{B}}\right.\right)$ equal to?

  Option A: $\frac{3}{7}$

  Option B: $\frac{3}{4}$

  Option C: $\frac{1}{3}$

  Option D: $\frac{4}{7}$

  VIEW SOLUTION

• Question 113
  A machine had three parts A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05, respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?

  Option A: 0.06

  Option B: 0.16

  Option C: 0.84

  Option D: 0.94

  VIEW SOLUTION

• Question 114
  Three independent events, A₁, A₂ and A₃ occur with probabilities $\mathrm{P}\left({\mathrm{A}}_i\right)=\frac{1}{1+i}, \mathrm{i}=1, 2, 3.$ What is the probability that at least one of the three events occurs?

  Option A: $\frac{1}{4}$

  Option B: $\frac{2}{3}$

  Option C: $\frac{3}{4}$

  Option D: $\frac{1}{24}$

  VIEW SOLUTION

• Question 115
  Two variance, x and y are uncorrelated and have standard deviations σ_x and σ_y respectively. What is the correlation coefficient between x + y and x – y?

  Option A: $\frac{{\sigma }_x\sigma y}{{\sigma }_x^2+{\sigma }_y^2}$

  Option B: $\frac{{\sigma }_x+{\sigma }_y}{2{\sigma }_x+{\sigma }_y}$

  Option C: $\frac{{\sigma }_x^2-{\sigma }_y^2}{{\sigma }_x^2+{\sigma }_y^2}$

  Option D: $\frac{{\sigma }_y-{\sigma }_x}{{\sigma }_x{\sigma }_y}$

  VIEW SOLUTION

• Question 116
  A random sample of 20 people is classified in the following table according to their ages :
   

  Age	Frequency
  15 – 25	2
  25 – 35	4
  35 – 45	6
  45 – 55	5
  55 – 65	3

  
  What is the mean age of this group of people?

  Option A: 41.0

  Option B: 41.5

  Option C: 42.0

  Option D: 42.5

  VIEW SOLUTION

• Question 117
  If the covariance between x and y is 30, variance of x is 25 and variance of y is 144, then what is the correlation coefficient?

  Option A: 0·4

  Option B: 0·5

  Option C: 0·6

  Option D: 0·7

  VIEW SOLUTION

• Question 118
  A coin is tossed three times. Consider the following events :
  A : No head appears
  B : Exactly one head appears
  C : At least two heads appear
  
  Which one of the following is correct?

  Option A: $(A\cup {\rm B})\cap (A\cup C)=B\cup C$

  Option B: $(A\cap {\rm B}\text{'})\cup (A\cap C\text{'})=B\text{'}\cup C\text{'}$

  Option C: ${\rm A}\cap (B\text{'}\cup C\text{'})=A\cup B\cup C$

  Option D: ${\rm A}\cap (B\text{'}\cup C\text{'})=B\text{'}\cap C\text{'}$

  VIEW SOLUTION

• Question 119
  In a series of 3 one-day cricket matches between terms A and B of a college, the probability of team A winning or drawing are 1/3 and 1/6, respectively. If a win, loss or draw gives 2, 0 and 1 point, respectively, then what is the probability that team A will score 5 points in the series?

  Option A: $\frac{17}{18}$

  Option B: $\frac{11}{12}$

  Option C: $\frac{1}{12}$

  Option D: $\frac{1}{18}$

  VIEW SOLUTION

• Question 120
  Let the random variable X follow B (6, p). If 16 P(X = 4) = P(X = 2), then what is the value of p?

  Option A: $\frac{1}{3}$

  Option B: $\frac{1}{4}$

  Option C: $\frac{1}{5}$

  Option D: $\frac{1}{6}$

  VIEW SOLUTION