List of practice Questions

Identify the sixth number in the series: 6, 11, 21, 36, 56, ?

Statements: All mangoes are golden in colour. No golden-coloured things are cheap. Conclusions: I. All mangoes are cheap. II. Golden-coloured mangoes are not cheap.

Find out the wrong number in the FOLLOWING series. 30, -5, -45, -90, -145, -195, -255

At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?

The minimum number of NAND gates required for implementing the Boolean expression, \( AB + ABC + AB\bar{C} \) is:

Fill in the banks with the correct option.

Technical writing demands \(\underline{\hspace{1cm}}\) use of language.

The passage states all the following about VR applications except

Choose the correct alternative with the correct choice given below each statement:

You are to conform \(\underline{\hspace{1cm}}\) the rules of the institute.

Choose the synonym. LIBERAL

"Bite the bullet" means

Which of the following alternatives to the underlined portion would NOT be acceptable?

The country cleared this \(\underline{\text{path and paved}}\) it with packed gravel...

Read the following sentence to find if there is any error in any part: (A) If I were him/ (B) I would teach/ (C) him a lesson/ (D) No error

If for some p, q, r ∈ R, not all have same sign, one of the roots of the equation (p² + q²)x² – 2q(p + r)x + q² + r² = 0 is also a root of the equation x² + 2x – 8 = 0, then (q² + r²)/p² is equal to _______ .

Angles of elevation of the top of a tower from three points (collinear) A, B and C on a road leading to the foot of the tower are 30\(^{\circ}\), 45\(^{\circ}\) and 60\(^{\circ}\) respectively. The ratio of AB and BC is

If the volume of the parallelepiped whose adjacent edges are \( \vec{a} = 2\hat{i} + 3\hat{j} + 4\hat{k} \), \( \vec{b} = \hat{i} + \alpha\hat{j} + 2\hat{k} \), \( \vec{c} = \hat{i} + 2\hat{j} + \alpha\hat{k} \) is 15, then \( \alpha \) is equal to

If \( 0 < P(A) < 1 \) and \( 0 < P(B) < 1 \), and \( P(A \cap B) = P(A)P(B) \), then

Area of the parallelogram formed by the lines \( y = 4x, y = 4x + 1, x + y = 0 \) and \( x + y = 1 \) is

For \( a \in \mathbb{R} \), \( a \neq -1 \), \( \lim_{n \to \infty} \frac{1^a + 2^a + \dots + n^a}{(n+1)^{a-1}[(na+1)+(na+2)+\dots+(na+n)]} = \frac{1}{60} \). Then one of the values of a is

The function \( f(x) = \log(x + \sqrt{x^2 + 1}) \) is

The area enclosed within the curve \( |x| + |y| = 2 \) is

Solutions of the equation \( \tan^{-1}\sqrt{x^2+x} + \sin^{-1}\sqrt{x^2+x+1} = \frac{\pi}{2} \) are

There are two circles in xy-plane whose equations are \( x^2 + y^2 - 2y = 0 \) and \( x^2 + y^2 - 2y - 3 = 0 \). A point (x, y) is chosen at random inside the larger circle. Then the probability that the point has been taken from smaller circle is

In a triangle ABC, if the tangent of half the difference of two angles is equal to one third of the tangent of half the sum of the angles, then the ratio of the sides opposite to the angles is

The eccentricity of an ellipse, with its center at the origin is \( \frac{1}{3} \). If one of the directrices is \( x = 9 \), then the equation of ellipse is:

Identify the fifth number in the series: 122, 144, 166, 188, ?