List of practice Questions

In an A.P., the product of the first term and the second term is 120 and the product of the second term and the third term is 168. Find the tenth term of the A.P. when common difference \(d>0\)
A metallic sphere of radius 8 cm is melted to form a cone with radius same as that of sphere. What is the height of the cone (in cm) ?
The value of the sum of 10 term of the series
\(S_{10}=\frac{1}{2^2-1}+\frac{1}{4^2-1}+\frac{1}{6^2-1}+...\)
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. \(\frac{3}{36}\)

Choose the correct answer from the options given below:
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 :