List of practice Questions

121.2 - 1.212 + 12.12

If \(y=\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+}}}}.....+\) then \(\frac{dy}{dx}\) is :

A matrix P of order 2 × 3 with each entry 0 or 1 and α is a scalar which is 3 or 4. If R = αA, the number of matrices R formed is :

If the transpose of matrix A is matrix B, where \(A=\begin{bmatrix} 2a & 1 & 3b \\ 1 & 2 & 4c \\ 5 & 6 & 0 \end{bmatrix}\)and \(B=\begin{bmatrix} 4 & 1 & 5 \\ 1 & 2 & 6 \\ 9 & 3 & 0 \end{bmatrix}\)then the value of 3a + 2b + 4c is :

The solution set of inequalities :
x + 3 ≤ 0 and 2x + 5 ≤ 0; if x ∈ R is :

The direction cosines of a line which makes equal angles with the co-ordinate axes is/are :

ABCD is a rhombus, whose diagonals intersect at E. Then \(\overrightarrow{EA}+\overrightarrow{EB}+\overrightarrow{EC}+\overrightarrow{ED}\) equals to :

The general solution of the differential equation xdy - ydx - 0 represents :

A flight from Delhi to Mumbai leaves every 5 hours. At the evening counter, it clarify that flight took off 25 minutes ago. If the time now is 10:40 am, what is the time for the next flight ?

A machine costing ₹ one lakh depreciates at constant rate 10%. Estimated useful life of machine is 8 years.
Match List I with List II

List I		List II
A.	Total depreciation in 2nd and 3rd year is	I.	₹81,000
B.	Value of machine after one year is	II.	₹17,100
C.	Value of machine after 2 year is	III.	₹43050
D.	Scrap value of machine is : given (1.1)3 - 2.144 & (0.9)3 - 0.4305	IV.	₹90,000

Choose the correct answer from the options given below :

The graph of the inequality 3x - 2y > 6 is

In a 1000 m race. A beats B by 50 meters or 10 seconds. The time taken by A to complete the race is :

If x = 4t², \(y=\frac{3}{t^3}\), then \(\frac{d^2y}{dx^2}\) at t = 1 is :

In a binomial distribution, the probability of getting a success is \(\frac{1}{3}\) and the standard deviation is 4. Then its mean is :

If \(3\begin{bmatrix} x&3\\2&1 \end{bmatrix}+4\begin{bmatrix} 1&2\\5&y \end{bmatrix}=\begin{bmatrix} 10&17\\26&11 \end{bmatrix}\)then the value of (3x+2y) is:

Match List I with List II

LIST I		LIST II
A.	The maximum value of the function \(f(x)=25x-\frac{5x^2}{2}+7\) in [-1,6] is	I.	24
B.	The minimum value of the function \(f(x)=2x^3-15x^2+36x+1\) in [1,5] is	II.	\(\frac{1}{16}\)
C.	The maximum value of the function \(f(x)=\frac{x}{2}-x^2\) in [0,1] is	III.	\(\frac{139}{2}\)
D.	The least value of the function \(f(x)=\frac{9}{x+3}+x\) in [-7,1], \(x\ne-3\) is	IV.	\(-\frac{37}{4}\)

Choose the correct answer from the options given below:

The probability distribution of a discrete random variable X is defined as:
\(P(X=x)=\begin{cases} 3kx & \text{for } x=1,2,3\\  5k(x+2) & \text{for } x=4,5 \\ 0& \text{otherwise}\end{cases}\)
The mean of the distribution is:

Consider the following hypothesis test
H₀: μ>=16
Η₁: μ < 16
A sample of 36 provided a sample mean of 15.4. The population standard deviation is 3. The value of the test statistic 't' is.

A random sample of size 9 has 21 as sample mean. The sum of the squares of the deviations taken from mean is 72. The sample is drawn from the population having 23 as mean. The value of test statistic is,

The maximum number of passengers an aeroplane can carry is 300. A profit of ₹1200 is made on each executive class ticket and a profit of ₹800 is made on each economy class ticket. The airline reserves atleast 40 seats for executive class. However, atleast 5 times as many passengers prefer to travel by economy class than by executive class. The maximum profit of the airline is:

If Laspeyre's index number is 225 and Paasche's index number is 144, then Fisher's ideal index number is:

The radius of the wheel of a vehicle is 35m. The wheel makes 10 revolutions in 6 seconds. The speed of the vehicle is :

Aman got 30% of the maximum marks in an examination and failed by 15% marks. However, Anil who took the same examination got 40% of the total marks and got 10 marks more than the passing marks. What were the passing marks in the examination ?

Akriti buys a smartphone for ₹ 12,500. If she wants to profit of 30%, how much should she charge for the smartphone ?

A pair of dice is thrown and sum of the numbers on two tosses is observed. Which of the statements are correct