List of practice Questions

If the straight lines \(x=1+s, y = -3-s, z=1+λs\) and \(x = \frac{t}{2},y=1+t, z=2-t\) with parameters s and t respectively, are coplanar, then \(λ\) is equal to:

If x is the least positive integer satisfying 100 ≡ x(mod 6), then (2x+1) is equal to :

If the matrix \(A =\begin{bmatrix}x&-2 &-5y\\ 2&0& -9 \\10& 3z &0\end{bmatrix}\)is skew-symmetric, then the value of \((2x-3y+4z)\) is:

Match List I with List II

Choose the correct answer from the options given below:

A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If P(X=1)=0.4, P(X=4)=P(X=2) and P(X=3)=2P(X=2), then P(X=0) is:

Consider the following data:

The equation of the straight line trend by the method of least squares is :

A car costing ₹8,00,000 has scrap value of ₹3,00,000. If the book value of car at the end of fourth year is ₹6,00,000, then the useful life of the car is:

In the equation of trend line \(y_t=a+bx\), a and b represent:

The area of a triangle is 9y cm². Find the value of y if its area is equal to the area of an equilateral triangle having side 6 cm.

If three vertices of a rhombus taken in order are (2, -1), (3, 4) and (-2, 3), then the fourth vertex is :

The mean and the median of a certain data are 13.3 and 13.5 respectively. Find the mode.

A man was allotted a work for 30 days on the condition that he would get ₹ 10 per day as wage if he reports for work and if he remains absent he would have to pay ₹ 2 as penalty for the day. Ultimately he got ₹ 216. For how many days he remained absent ?

In the figure, O is centre of the circle. What is the measure of ∠ABC ?

If perimeter of a rhombus is 104 cm and length of one of its diagonals is 48 cm, then area of the rhombus (in cm²) is:

Find the median of the following data: \(42, 19, 46, 17, 8, 35, 26, 39, 29\)

Find the average of squares of first five natural numbers.

A thief is spotted by a policeman from a distance of \(200 \)meters. The policeman starts chasing at a speed of \( 10 \frac{km}{h}\) while the thief is running at a speed of \( 8\frac{km}{h}\). After how much time (in minutes) will the thief be caught?

A ladder 25 feet long is leaning against a wall such that it touches 24 feet high window. How far is the foot of the ladder from the wall?

If the points (2, -3), (λ, -1) and (0, 4) are collinear, then the value of λ is :

If \(f(x)=\begin{cases} 2x+8, & 1\le x\le2 \\ 6x, & 2\lt x \lt4\end{cases}\), then \(\int_1^4f(x)\) is :

The principal value of \(\sin^{-1}(\frac{1}{2})\) is :

The value of λ for which the matrix \(\begin{pmatrix} 1 & 0 & λ \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{pmatrix}\) is a singular matrix is :

If \(a:b=\frac{2}{3}:\frac{1}{4}\) and \(b:c=\frac{3}{4}:\frac{4}{5}\) then find a : b : c.

In what ratio the line segment joining the points (-2, 3) and (3, -7) is divided by x-axis ?

Find the average of first 10 prime numbers.