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Q1:

The corner points of the feasible region determined by x+y≤8,2x+y≥8,x≥0,y≥0x+y \leq 8, 2 x+y \geq 8, x \geq 0, y \geq 0 are A(0,8),B(4,0)A(0,8), B(4,0) and C(8,0)C(8,0). If the objective function Z=ax+Z=a x+ by has its maximum value on the line segment ABA B, then the relation between aa and bb is :
Answer options
Option: 2
Correct Answer
Explanation →

Q2:

If t=e2xt=e^{2 x} and y=log⁡et2y=\log _{e} t^{2}, then d2ydx2\frac{d^{2} y}{d x^{2}} is :
Answer options
Option: 1
Correct Answer
Explanation →

Q3:

An objective function Z=ax+byZ=a x+b y is maximum at points (8,2)(8,2) and (4,6)(4,6). If a≥0a \geq 0 and b≥0b \geq 0 and ab=25a b=25, then the maximum value of the function is equal to :
Answer options
Option: 2
Correct Answer
Explanation →

Q4:

The area of the region bounded by the lines x+2y=12,x=2,x=6x+2 y=12, x=2, x=6 and xx-axis is :
Answer options
Option: 4
Correct Answer
Explanation →

Q5:

A die is rolled thrice. What is the probability of getting a number greater than 44 in the first and the second throw of dice and a number less than 44 in the third throw ?
Answer options
Option: 4
Correct Answer
Explanation →

Q6:

∫πxn+1−xdx=\int \dfrac{\pi}{x^{n+1}-x} d x=
Answer options
Option: 1
Correct Answer
Explanation →

Q7:

The value of ∫01a−bx2(a+bx2)2dx\int_{0}^{1} \frac{a-b x^{2}}{\left(a+b x^{2}\right)^{2}} d x is :
Answer options
Option: 4
Correct Answer
Explanation →

Q8:

The second order derivative of which of the following functions is 5x5^{\mathrm{x}} ?
Answer options
Option: 4
Correct Answer
Explanation →

Q9:

The degree of the differential equation (1−(dydx)2)32=kd2ydx2\left(1-\left(\frac{d y}{d x}\right)^{2}\right)^{\frac{3}{2}}=k \frac{d^{2} y}{d x^{2}} is :
Answer options
Option: 2
Correct Answer
Explanation →

Q10:

If AA and BB are symmetric matrices of the same order, then AB−BAA B-B A is a :
Answer options
Option: 3
Correct Answer
Explanation →

Q11:

If AA is a square matrix of order 44 and ∣A∣=4|A|=4, then ∣2A∣|2 A| will be :
Answer options
Option: 2
Correct Answer
Explanation →

Q12:

If [A]3×2[ B]x×y=[C]3×1[\mathrm{A}]_{3 \times 2}[\mathrm{~B}]_{\mathrm{x} \times \mathrm{y}}=[\mathrm{C}]_{3 \times 1}, then :
Answer options
Option: 2
Correct Answer
Explanation →

Q13:

If a function f(x)=x2+bx+1f(x)=x^{2}+b x+1 is increasing in the interval [1,2][1,2], then the least value of bb is :
Answer options
Option: 3
Correct Answer
Explanation →

Q14:

Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be :
Answer options
Option: 2
Correct Answer
Explanation →

Q15:

For the function f(x)=2x3−9x2+12x−5f(x) = 2x^3 - 9x^2 + 12x - 5, x∈[0,3]x \in [0, 3], match List-I with List-II :
List-I List-II
A. Absolute maximum value (I) 3 3
B. Absolute minimum value (II) 0 0
C. Point of maxima (III) −5 -5
D. Point of minima (IV) 4 4
Answer options
Option: 4
Correct Answer
Explanation →

Q16:

The rate of change (in cm2/s\mathrm{cm}^{2} / \mathrm{s} ) of the total surface area of a hemisphere with respect to radius rr at r=1.3313 cmr=\sqrt[3]{1.331} \mathrm{~cm} is :
Answer options
Option: 2
Correct Answer
Explanation →

Q17:

The area of the region bounded by the lines x73a+yb=4,x=0\frac{x}{7 \sqrt{3} a}+\frac{y}{b}=4, x=0 and y=0y=0 is :
Answer options
Option: 1
Correct Answer
Explanation →

Q18:

If AA is a square matrix and II is an identity matrix such that A2=AA^{2}=A, then A(I−2A)3+2A3A(I-2 A)^{3}+2 A^{3} is equal to :
Answer options
Option: 4
Correct Answer
Explanation →

Q19:

The value of the integral ∫log⁡e2log⁡e3e2x−1e2x+1dx\int_{\log _{e} 2}^{\log _{e} 3} \frac{e^{2 x}-1}{e^{2 x}+1} d x is :
Answer options
Option: 2
Correct Answer
Explanation →

Q20:

If a⃗,b⃗\vec{a}, \vec{b} and c⃗\vec{c} are three vectors such that a⃗+b⃗+c⃗=0→\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}, where a⃗\vec{a} and b⃗\vec{b} are unit vectors and ∣c⃗∣=2|\vec{c}|=2, then the angle between the vectors b⃗\vec{b} and c⃗\vec{c} is :
Answer options
Option: 4
Correct Answer
Explanation →

Q21:

Let [x][x] denote the greatest integer function. Then match List-I with List-II:

\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline
List-I List-II
(A) ∣x−1∣+∣x−2∣ |x - 1| + |x - 2| (I) is differentiable everywhere except at x=0 x = 0
(B) x−∣x∣ x - |x| (II) is continuous everywhere
(C) x−[x] x - [x] (III) is not differentiable at x=1 x = 1
(D) x ∣x∣ x \, |x| (IV) is differentiable at x=1 x = 1
Answer options
Option: 3
Correct Answer
Explanation →

Q22:

Choose the correct answer from the options given below:
List-I List-II
(A) Integrating factor of x dy−(y+2x2) dx=0 x \, dy - (y + 2x^2) \, dx = 0 (I) 1x \frac{1}{x}
(B) Integrating factor of (2x2−3y) dx=x dy (2x^2 - 3y) \, dx = x \, dy (II) x x
(C) Integrating factor of (2y+3x2) dx+x dy=0 (2y + 3x^2) \, dx + x \, dy = 0 (III) x2 x^2
(D) Integrating factor of 2x dy+(3x3+2y) dx=0 2x \, dy + (3x^3 + 2y) \, dx = 0 (IV) x3 x^3
Answer options
Option: 2
Correct Answer
Explanation →

Q23:

If the function f:N→Nf: \mathbb{N} \rightarrow \mathbb{N} is defined as f(n)={n−1, if n is even n+1, if n is odd f(n)=\left\{\begin{array}{ll}n-1, & \text { if } n \text { is even } \\ n+1, & \text { if } n \text { is odd }\end{array}\right., then \newline (A) f is injective \newline (B) f is into \newline (C) f is surjective \newline (D) f is invertible
Answer options
Option: 4
Correct Answer
Explanation →

Q24:

∫0π21−cot⁡xcosec⁡x+cos⁡xdx=\int_{0}^{\frac{\pi}{2}} \frac{1-\cot x}{\operatorname{cosec} x+\cos x} d x=
Answer options
Option: 1
Correct Answer
Explanation →

Q25:

If the random variable X X has the following distribution:
X X 0 1 2 otherwise
P(X) P(X) k k 2k 2k 3k 3k 0 0
Match List-I with List-II:
List-I List-II
(A) k k (I) 56 \frac{5}{6}
(B) P(X<2) P(X < 2) (II) 43 \frac{4}{3}
(C) E(X) E(X) (III) 12 \frac{1}{2}
(D) P(1≤X≤2) P(1 \leq X \leq 2) (IV) 16 \frac{1}{6}
Answer options
Option: 2
Correct Answer
Explanation →

Q26:

For a square matrix An×nA_{n \times n}
(A) ∣adj⁡A∣=∣A∣n−1|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^{\mathrm{n}-1}
(B) ∣A∣=∣adj⁡A∣n−1|\mathrm{A}|=|\operatorname{adj} \mathrm{A}|^{\mathrm{n}-1}
(C) A(adj⁡A)=∣A∣\mathrm{A}(\operatorname{adj} \mathrm{A})=|\mathrm{A}|
(D) ∣A−1∣=1∣ A∣\left|\mathrm{A}^{-1}\right|=\frac{1}{|\mathrm{~A}|}
Answer options
Option: 2
Correct Answer
Explanation →

Q27:

The matrix [100010001]\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] is a : \newline (A) scalar matrix \newline (B) diagonal matrix \newline (C) skew-symmetric matix \newline (D) symmetric matrix
Choose the correct answer from the options given below :
Answer options
Option: 1
Correct Answer
Explanation →

Q28:

The feasible region represented by the constraints 4x+y≥80,x+5y≥115,3x+2y≤150,x,y≥04 x+y \geq 80, x+5 y \geq 115,3 x+2 y \leq 150, x, y \geq 0 of an LPP is
Answer options
Option: 3
Correct Answer
Explanation →

Q29:

The area of the region enclosed between the curves 4x2=y4 x^{2}=y and y=4y=4 is :
Answer options
Option: 4
Correct Answer
Explanation →

Q30:

∫ex(2x+12x)dx\int \mathrm{e}^{\mathrm{x}}\left(\frac{2 \mathrm{x}+1}{2 \sqrt{\mathrm{x}}}\right) \mathrm{dx}
Answer options
Option: 4
Correct Answer
Explanation →

Q31:

If f(x)f(x), defined by f(x)={kx+1 if x≤πcos⁡x if x>πf(x)=\left\{\begin{array}{lll}k x+1 & \text { if } & x \leq \pi \\ \cos x & \text { if } & x>\pi\end{array}\right. is continuous at x=πx=\pi, then the value of kk is :
Answer options
Option: 4
Correct Answer
Explanation →

Q32:

If P=[−121]P=\left[\begin{array}{r}-1 \\ 2 \\ 1\end{array}\right] and Q=[2−41]Q=\left[\begin{array}{lll}2 & -4 & 1\end{array}\right] are two matrices, then (PQ)′(P Q)^{\prime} will be :
Answer options
Option: 2
Correct Answer
Explanation →

Q33:

Δ=∣1cos⁡x1−cos⁡x1cos⁡x−1−cos⁡x1∣\Delta=\left|\begin{array}{ccc}1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1\end{array}\right|
(A) Δ=2(1−cos⁡2x)\Delta=2\left(1-\cos ^{2} x\right)
(B) Δ=2(2−sin⁡2x)\Delta=2\left(2-\sin ^{2} x\right)
(C) Minimum value of Δ\Delta is 22
(D) Maximum value of Δ\Delta is 44
Choose the correct answer from the options given below :
Answer options
Option: 4
Correct Answer
Explanation →

Q34:

f(x)=sin⁡x+12cos⁡2x in [0,π2]f(x)=\sin x+\frac{1}{2} \cos 2 x \text { in }\left[0, \frac{\pi}{2}\right]
(A) f′(x)=cos⁡x−sin⁡2xf^{\prime}(x)=\cos x-\sin 2 x
(B) The critical points of the function are x=π6x=\frac{\pi}{6} and x=π2x=\frac{\pi}{2}
(C) The minimum value of the function is 22
(D) The maximum value of the function is 34\frac{3}{4}
Choose the correct answer from the options given below :
Answer options
Option: 1
Correct Answer
Explanation →

Q35:

The direction cosines of the line which is perpendicular to the lines with direction ratios 1,−2,−21,-2,-2 and 0,2,10,2,1 are :
Answer options
Option: 1
Correct Answer
Explanation →

Q36:

Let XX denote the number of hours you play during a randomly selected day. The probability that XX can take values xx has the following form, where cc is some constant.
P(X=x)={0.1, if x=0cx, if x=1 or x=2c(5−x), if x=3 or x=40, otherwise \mathrm{P}(\mathrm{X}=\mathrm{x})=\left\{\begin{array}{lll} 0.1, & \text { if } \mathrm{x}=0 \\ \mathrm{cx}, & \text { if } \mathrm{x}=1 \text { or } \mathrm{x}=2 \\ \mathrm{c}(5-\mathrm{x}), & \text { if } \mathrm{x}=3 \text { or } \mathrm{x}=4 \\ 0, & \text { otherwise } \end{array}\right.
Match List-I with List-II :
List-I List-II
(A) c c (I) 0.75
(B) P(X≤2) P(X \leq 2) (II) 0.3
(C) P(X=2) P(X = 2) (III) 0.55
(D) P(X≥2) P(X \geq 2) (IV) 0.15
Answer options
Option: 2
Correct Answer
Explanation →

Q37:

If sin⁡y=xsin⁡(a+y)\sin y=x \sin (a+y), then dydx\frac{d y}{d x} is :
Answer options
Option: 4
Correct Answer
Explanation →

Q38:

The unit vector perpendicular to each of the vectors a⃗+b⃗\vec{a}+\vec{b} and a⃗−b⃗\vec{a}-\vec{b}, where a⃗=i^+j^+k^\vec{a}=\hat{i}+\hat{j}+\hat{k} and b⃗=i^+2j^+3k^\vec{b}=\hat{i}+2 \hat{j}+3 \hat{k}, is :
Answer options
Option: 4
Correct Answer
Explanation →

Q39:

The distance between the lines r⃗=i^−2j^+3k^+λ(2i^+3j^+6k^)\vec{r}=\hat{i}-2 \hat{j}+3 \hat{k}+\lambda(2 \hat{i}+3 \hat{j}+6 \hat{k}) and r⃗=3i^−2j^+1k^+μ(4i^+6j^+12k^)\vec{r}=3 \hat{i}-2 \hat{j}+1 \hat{k}+\mu(4 \hat{i}+6 \hat{j}+12 \hat{k}) is :
Answer options
Option: 3
Correct Answer
Explanation →

Q40:

If f(x)=2(tan⁡−1(ex)−π4)f(x)=2\left(\tan ^{-1}\left(e^{x}\right)-\frac{\pi}{4}\right), then f(x)f(x) is :
Answer options
Option: 3
Correct Answer
Explanation →

Q41:

For the differential equation (xlog⁡ex)dy=(log⁡ex−y)dx\left(x \log _{e} x\right) d y=\left(\log _{e} x-y\right) d x
(A) Degree of the given differential equation is 11.
(B) It is a homogeneous differential equation.
(C) Solution is 2ylog⁡ex+A=(log⁡ex)22y \log _{\mathrm{e}} \mathrm{x}+A=\left(\log _{\mathrm{e}} \mathrm{x}\right)^{2}, where AA is an arbitrary constant
(D) Solution is 2ylog⁡ex+A=log⁡e(log⁡ex)2 y \log _{e} x+A=\log _{e}\left(\log _{e} x\right), where AA is an arbitrary constant
Choose the correct answer from the options given below :
Answer options
Option: 1
Correct Answer
Explanation →

Q42:

There are two bags. Bag-1 contains 44 white and 66 black balls and Bag-2 contains 55 white and 55 black balls. A die is rolled, if it shows a number divisible by 3, a ball is drawn from Bag-1, else a ball is drawn from Bag-2. If the ball drawn is not black in colour, the probability that it was not drawn from Bag-2 is :
Answer options
Option: 3
Correct Answer
Explanation →

Q43:

Which of the following cannot be the direction ratios of the straight line x−32=2−y3=z+4−1\frac{x-3}{2}=\frac{2-y}{3}=\frac{z+4}{-1} ?
Answer options
Option: 3
Correct Answer
Explanation →

Q44:

Which one of the following represents the correct feasible region determined by the following constraints of an LPP? \newline x+y≥10,2x+2y≤25,x≥0,y≥0x+y \geq 10,2 x+2 y \leq 25, x \geq 0, y \geq 0
Answer options
Option: 3
Correct Answer
Explanation →

Q45:

Let R be the relation over the set A of all straight lines in a plane such that l1Rl2⇔l1l_{1} \mathrm{R} l_{2} \Leftrightarrow l_{1} is parallel to l2l_{2}. Then R is :
Answer options
Option: 2
Correct Answer
Explanation →

Q46:

The probability of not getting 5353 Tuesdays in a leap year is :
Answer options
Option: 4
Correct Answer
Explanation →

Q47:

The angle between two lines whose direction ratios are propotional to 1,1,−21,1,-2 and (3−1),(−3−1),−4(\sqrt{3}-1),(-\sqrt{3}-1),-4 is :
Answer options
Option: 1
Correct Answer
Explanation →

Q48:

If (a⃗−b⃗)⋅(a⃗+b⃗)=27(\vec{a}-\vec{b}) \cdot(\vec{a}+\vec{b})=27 and ∣a⃗∣=2∣b⃗∣|\vec{a}|=2|\vec{b}|, then ∣b⃗∣|\vec{b}| is :
Answer options
Option: 1
Correct Answer
Explanation →

Q49:

If tan⁡−1(23−x+1)=cot⁡−1(33x+1)\tan ^{-1}\left(\frac{2}{3^{-x}+1}\right)=\cot ^{-1}\left(\frac{3}{3^{x}+1}\right), then which one of the following is true ?
Answer options
Option: 2
Correct Answer
Explanation →

Q50:

If A,BA, B and CC are three singular matrices given by A=[1432a],B=[3b5a2]A=\left[\begin{array}{ll}1 & 4 \\ 3 & 2 a\end{array}\right], B=\left[\begin{array}{ll}3 b & 5 \\ a & 2\end{array}\right] and C=[a+b+cc+1a+cc]C=\left[\begin{array}{cc}a+b+c & c+1 \\ a+c & c\end{array}\right], then the value of abca b c is :
Answer options
Option: 3
Correct Answer
Explanation →

Q51:

A random variable XX has the following probability distribution :
X X 1 2 3 4 5 6 7
P(X) P(X) k k 2k 2k 2k 2k 3k 3k k2 k^2 2k22k^2 7k2+k7k^2+k
Match the options of List-I to List-II :
List-I List-II
(A) k k (I) 710 \frac{7}{10}
(B) P(X<3) P(X < 3) (II) 53100 \frac{53}{100}
(C) P(X>2) P(X > 2) (III) 110 \frac{1}{10}
(D) P(2<X<7) P(2 < X <7 ) (IV) 310 \frac{3}{10}
Choose the correct answer from the options given below :
Answer options
Option: 4
Correct Answer
Explanation →

Q52:

Match List-I with List-II :
List-I \\ (Function) List-II \\ (Derivative w.r.t. x)
(A) 5xlog⁡e5 \frac{5^x}{\log _ e 5} (I) 5x(log⁡e5)2 5^x(\log _ e5)^2
(B) log⁡e5 \log _ e 5 (II) 5xlog⁡e55^x \log _ e 5
(C) 5xlog⁡e5 5^x\log _ e 5 (III) 5x 5^x
(D) 5x 5^x (IV) 0 0
Choose the correct answer from the options given below :
Answer options
Option: 4
Correct Answer
Explanation →

Q53:

For which one of the following purposes is CAGR (Compounded Annual Growth Rate) not used ?
Answer options
Option: 2
Correct Answer
Explanation →

Q54:

A flower vase costs ₹ 36,00036,000. With an annual depreciation of ₹ 2,0002,000, its cost will be ₹ 6,0006,000 in _____ years.
Answer options
Option: 2
Correct Answer
Explanation →

Q55:

Arun's speed of swimming in still water is 5 km/hr5 \mathrm{~km} / \mathrm{hr}. He swims between two points in a river and returns back to the same starting point. He took 2020 minutes more to cover the distance upstream than downstream. If the speed of the stream is 2 km/hr2 \mathrm{~km} / \mathrm{hr}, then the distance between the two points is :
Answer options
Option: 3
Correct Answer
Explanation →

Q56:

If ey=xx\mathrm{e}^{\mathrm{y}}=\mathrm{x}^{\mathrm{x}}, then which of the following is true ?
Answer options
Option: 4
Correct Answer
Explanation →

Q57:

The probability of a shooter hitting a target is 34\frac34. How many minimum number of times must he fire so that the probability of hitting the target at least once is more than 90%90 \% ?
Answer options
Option: 2
Correct Answer
Explanation →

Q58:

List I List II
(A) Distribution of a sample leads to becoming a normal distribution (I) Central Limit Theorem
(B) Some subset of the entire population (III) Sample
(C) Population mean (IV) Parameter
(D) Some assumptions about the population (II) Hypothesis
Choose the correct answer from the options given below :-
Answer options
Option: 2
Correct Answer
Explanation →

Q59:

Ms. Sheela creates a fund of ₹ 1,00,0001,00,000 for providing scholarships to needy children. The scholarship is provided in the beginning of the year. This fund earns an interest of r%r \% per annum. If the scholarship amount is taken as ₹ 8,0008,000, then r=r=
Answer options
Option: 2
Correct Answer
Explanation →

Q60:

A person wants to invest an amount of ₹ 75,00075,000. He has two options A and B yielding 8%8 \% and 9%9 \% return respectively on the invested amount. He plans to invest at least ₹ 15,00015,000 in Plan A and at least ₹ 25,00025,000 in Plan B. Also he wants that his investment in Plan A is less than or equal to his investment in Plan B. Which of the following options describes the given LPP to maximize the return (where xx and yy are investments in Plan A and Plan B respectively) ?
Answer options
Option: 4
Correct Answer
Explanation →

Q61:

In a 700 m700 \mathrm{~m} race, Amit reaches the finish point in 2020 seconds and Rahul reaches in 2525 seconds. Amit beats Rahul by a distance of :
Answer options
Option: 3
Correct Answer
Explanation →

Q62:

For the given five values 12,15,18,24,3612,15,18,24,36; the three-year moving averages are :
Answer options
Option: 3
Correct Answer
Explanation →

Q63:

A property dealer wishes to buy different houses given in the table below with some down payments and balance in EMI for 2525 years. Bank charges 6%6\% per annum compounded monthly.
Given: (1.005)300×0.005(1.005)300−1=0.0064\dfrac{(1.005)^{300} \times 0.005}{(1.005)^{300}-1}=0.0064
Property type Price of the property (in ₹) Down Payment (in ₹)
P 45,00,000 5,00,000
Q 55,00,000 5,00,000
R 65,00,000 10,00,000
S 75,00,000 15,00,000
Match List-I with List-II:
List-I
Property Type		 List-II
EMI amount (in ₹)
(A) P (I) 25,600
(B) Q (II) 38,400
(C) R (III) 32,000
(D) S (IV) 35,200
Answer options
Option: 2
Correct Answer
Explanation →

Q64:

The corner points of the feasible region for an L.P.P. are (0,10),(5,5),(5,15)(0,10),(5,5),(5,15) and (0,30)(0,30). If the objective function is Z=αx+βy,α,β>0Z=\alpha x+\beta y, \alpha, \beta>0, the condition on α\alpha and β\beta so that maximum of ZZ occurs at corner points (5,5)(5,5) and (0,20)(0,20) is :
Answer options
Option: 3
Correct Answer
Explanation →

Q65:

The solution set of the inequality ∣3x∣≥∣6−3x∣|3 x| \geq|6-3 x| is :
Answer options
Option: 2
Correct Answer
Explanation →

Q66:

If the matrix [0−13x1y−5−650]\left[\begin{array}{rrr}0 & -1 & 3 x \\ 1 & y & -5 \\ -6 & 5 & 0\end{array}\right] is skew-symmetric, then the value of 5x−y5 x-y is:
Answer options
Option: 3
Correct Answer
Explanation →

Q67:

A company is selling a certain commodity xx. The demand function for the commodity is linear. The company can sell 20002000 units when the price is ₹88 per unit and it can sell 30003000 units when the price is ₹44 per unit. The Marginal revenue at x=5x=5 is:
Answer options
Option: 2
Correct Answer
Explanation →

Q68:

If the lengths of the three sides of a trapezium other than the base are 10 cm10 \mathrm{~cm} each, then the maximum area of the trapezium is:
Answer options
Option: 3
Correct Answer
Explanation →

Q69:

Three defective bulbs are mixed with 88 good ones. If three bulbs are drawn one by one with replacement, the probabilities of getting exactly 11 defective, more than 22 defective, no defective and more than 11 defective respectively are:
Answer options
Option: 3
Correct Answer
Explanation →

Q70:

If A=[2443],X=[n1],B=[811]\mathrm{A}=\left[\begin{array}{ll}2 & 4 \\ 4 & 3\end{array}\right], \mathrm{X}=\left[\begin{array}{l}\mathrm{n} \\ 1\end{array}\right], \mathrm{B}=\left[\begin{array}{c}8 \\ 11\end{array}\right] and AX=BA X=B, then the value of nn will be :
Answer options
Option: 3
Correct Answer
Explanation →

Q71:

The equation of the tangent to the curve x52+y52=33\mathrm{x}^{\frac{5}{2}}+\mathrm{y}^{\frac{5}{2}}=33 at the point (1,4)(1,4) is :
Answer options
Option: 1
Correct Answer
Explanation →

Q72:

X X -2 -1 0 1 2
P(X) P(X) 0.2 0.2 0.1 0.1 0.3 0.3 0.2 0.2 0.20.2
The variance of XX will be :
Answer options
Option: 3
Correct Answer
Explanation →

Q73:

A Multinational company creates a sinking fund by setting a sum of ₹ 12,00012,000 annually for 1010 years to pay off a bond issue of ₹ 72,00072,000. If the fund accumulates at 5%5 \% per annum compound interest, then the surplus after paying for bond is :
(Use (1.05)10≈1.6)\left.(1.05)^{10} \approx 1.6\right)
Answer options
Option: 3
Correct Answer
Explanation →

Q74:

The least non-negative remainder when 3513^{51} is divided by 77 is :
Answer options
Option: 3
Correct Answer
Explanation →

Q75:

If [5x+87y+310x+12]=[23y+150]\left[\begin{array}{cc}5 x+8 & 7 \\ y+3 & 10 x+12\end{array}\right]=\left[\begin{array}{cc}2 & 3 y+1 \\ 5 & 0\end{array}\right], then the value of 5x+3y5 x+3 y is equal to :
Answer options
Option: 4
Correct Answer
Explanation →

Q76:

There are 66 cards numbered 11 to 66, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two cards drawn. Then P(X>3)\mathrm{P}(\mathrm{X}>3) is :
Answer options
Option: 1
Correct Answer
Explanation →

Q77:

Which of the following are components of a time series ? \newline (A) Irregular component \newline (B) Cyclical component \newline (C) Chronological Component \newline (D) Trend Component
Choose the correct answer from the options given below :
Answer options
Option: 1
Correct Answer
Explanation →

Q78:

The following data is from a simple random sample : \newline 15,23,x,37,19,3215,23, x, 37,19,32
If the point estimate of the population mean is 2323, then the value of xx is :
Answer options
Option: 1
Correct Answer
Explanation →

Q79:

For an investment, if the nominal rate of interest is 10%10 \% compounded half yearly, then the effective rate of interest is :
Answer options
Option: 1
Correct Answer
Explanation →

Q80:

A mixture contains apple juice and water in the ratio 10:x10: \mathrm{x}. When 3636 litres of the mixture and 99 litres of water are mixed, the ratio of apple juice and water becomes 5:45: 4. The value of xx is :
Answer options
Option: 2
Correct Answer
Explanation →

Q81:

For I=[1001]I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right], if XX and YY are square matrices of order 22 such that XY=XX Y=X and YX=YY X=Y, then (Y2+2Y)\left(\mathrm{Y}^{2}+2 \mathrm{Y}\right) equals to :
Answer options
Option: 4
Correct Answer
Explanation →

Q82:

A coin is tossed K times. If the probability of getting 33 heads is equal to the probability of getting 77 heads, then the probability of getting 88 tails is :
Answer options
Option: 3
Correct Answer
Explanation →

Q83:

If 95%95 \% confidence interval for the population mean was reported to be 160160 to 170170 and σ=25\sigma=25, then size of the sample used in this study is: (Given Z0.025=1.96\mathrm{Z}_{0.025}=1.96 )
Answer options
Option: 1
Correct Answer
Explanation →

Q84:

Two pipes A and B together can fill a tank in 4040 minutes. Pipe A is twice as fast as pipe B. Pipe A alone can fill the tank in :
Answer options
Option: 1
Correct Answer
Explanation →

Q85:

An even number is the determinant of \newline (A) [1−1−15]\left[\begin{array}{rr}1 & -1 \\ -1 & 5\end{array}\right]
(B) [13−1−115]\left[\begin{array}{cc}13 & -1 \\ -1 & 15\end{array}\right]
(C) [16−1−1115]\left[\begin{array}{rr}16 & -1 \\ -11 & 15\end{array}\right]
(D) [6−121115]\left[\begin{array}{rr}6 & -12 \\ 11 & 15\end{array}\right]
Choose the correct answer from the options given below :
Answer options
Option: 1
Correct Answer
Explanation →

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