List of practice Questions

A 300 m long train is moving at a speed of 60 km/h. In what time will it cross a single pole?
A piece of paper is folded and a cut is made as shown below. How it will appear when opened?
A piece of paper is folded and a cut is made
Domain of function \(f(x) = cos^{-1}\sqrt {2x-1}\) is
For the LPP, Min \(Z= 5x + 7y\) subject to \(x≥0, y≥0; 2x+y≥8, x+2y≥ 10,\) the basic feasible solutions are:
Match List I with List II
LIST I LIST II
A.\(\frac{d}{dx} [tan^{-1} (\frac{3x-x^3}{1-3x^2})]\)I.\(\frac{3}{1+x^2}\)
B.\(\frac{d}{dx}[cos^{-1}(\frac{1-x^2}{1+x^2})]\)II.\(\frac{-3}{1+x^2}\)
C.\(\frac{d}{dx}[cos^{-1} (\frac{2x}{1+x^2})]\)III.\(\frac{-2}{1+x^2}\)
D.\(\frac{d}{dx}[cot^{-1}(\frac{3x-x^3}{1-3x^2})]\)IV.\(\frac{2}{1+x^2}\)
Choose the correct answer from the options given below:
Let A and B be symmetric matrices of same order, then which of the following statement is true?
If, \(f(x) = \begin{bmatrix}0 & x-a & x-b \\[0.3em]x+a&o & x-c \\[0.3em]x+b & x+c & 0\\[0.3em] \end{bmatrix}\), then \(f(0)\) is:
The radius of a spherical ball is increasing at the rate of 1 m/sec. At the radius equal to 3m, the volume of the ball is increasing at the rate given by:
The value of \(\lambda\), for which the projection of \(\vec{a} = \lambda \hat{i} + \hat{j} +4 \hat{k}\) on \(\vec{b} =2\hat{i} +6 \hat{j} +3\hat{k}\) is 4 units
Let a pair of dice be thrown and the random variable X be the sum of numbers on the two dice. Then.
Match List I with List II.
List IList II
A. P (X = 2)I. \(\frac{4}{36}\)
B. P (X = 4)II. \(\frac{5}{36}\)
C. P (X - 5)III. \(\frac{1}{36}\)
D. P (X - 6)IV. \(\frac{3}{36}\)

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If \(|A|=3\)  and \(A^{-1}=\begin{bmatrix}        3 &-1 \\[0.3em]        \frac{-5}{3} & \frac{2}{3}    \\[0.3em]     \end{bmatrix}\) then adj \(A\) is 
The value of the determinant \(\begin{vmatrix}acosθ&bsinθ&0 \\-bsinθ&acosθ&0\\ 0&0&c\end{vmatrix}\) is:
The differential equation whose solution is Ax2+By2=1 where A and B are arbitrary constant is of:
(A) first order and first degree
(B) second order and first degree
(C) second order and second degree
(D) second order
Choose the correct answer from the options given below:
The inverse of the function f: R→R given by f(x) = 2x +7 is:
Consider the following hypothesis test:
\(Η_0: μ ≤ 20\)
\(Η_1 : μ > 20\)
A sample of 81 produced a sample mean of 20.55. The population standard deviation is 3. The value of the test statistic is:
Two years ago, population of a city was \(16,52,600 \)which increased by \( 10\%\) in the first year and by \(15\%\) in the second year. Find the present population of the city.
Which of the following speeds is maximum?
If y = \(10^{10^x}\), then \(\frac{dy}{dx}\) is :
The area of the region bounded by the curve \(y=\sqrt{3x+10}\), x-axis and between the lines x = -3 and x = 2 is equal to :
If each side of a cube is x, then the angle between the diagonals of the cube is :
Set A has elements and the set B has 6 elements, then the number of injective mappings that can be defined from A to B is :
The price per unit of a commodity produced by a company is given by P = 92 - 2x2, where x is the quantity demanded. The marginal revenue of producing 3 units of such a commodity shall be :
Simplify \(\sqrt{54-\sqrt{20+\sqrt{32-\sqrt{49}}}}\)
A's month salary was ₹40000 and he used to save ₹10000 per month. His salary increased by 25% and expenditure increased by 15%. By what percent his savings increased ?
What is emprical relationship between mean, median and mode ?
A. Mean - mode = 3(Mean - Median)
B. Mode = Mean - Median
C. Mode = 3 Median - 2 Mean
D. Median - Mode = 3 (Mean - Median)
E. Mode = 2 Mean + 3 Median
Choose the correct answer from the options given below