List of practice Questions

The acceleration of a particle which moves along the positive \( x \)-axis varies with its position as shown in the figure. If the velocity of the particle is \( 0.8 \, {m/s} \) at \( x = 0 \), then its velocity at \( x = 1.4 \, {m} \) is: \includegraphics[]{83.png}
The triangle \( PQR \) is inscribed in the circle \[ x^2 + y^2 = 25. \] If \( Q = (3,4) \) and \( R = (-4,3) \), then \( \angle QPR \) is:
If \( A(1,2,0), B(2,0,1), C(-3,0,2) \) are the vertices of \( \triangle ABC \), then the length of the internal bisector of \( \angle BAC \) is:
p-Methyl benzene nitrile can be prepared from which of the following?
Two ideal gases A and B of the same number of moles expand at constant temperatures \( T_1 \) and \( T_2 \) respectively such that the pressure of gas A decreases by \( 50% \) and the pressure of gas B decreases by \( 75% \). If the work done by both the gases is the same, then the ratio \( T_1:T_2 \) is:
If all chords of the curve \( 2x^2 - y^2 + 3x + 2y = 0 \), which subtend a right angle at the origin, always pass through the point \( (a, \beta) \), then \( (a, \beta) = \):
If \( z_1 = 10 + 6i \), \( z_2 = 4 + 6i \) and \( z \) is any complex number such that the argument of \( \frac{z-z_1}{z-z_2} \) is \( \frac{\pi}{4} \), then the value of \( |z - 7 - 9i| \) is:
Two blocks of equal masses are tied with a light string passing over a massless pulley (Assuming frictionless surfaces). The acceleration of the centre of mass of the two blocks is (Given \( g = 10 \, \text{m/s}^2 \)):
Two blocks of equal masses are tied
There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle, then the number of such possible arrangements is:
A diving board is at a height of \( h \) from the water surface. A swimmer standing on this board throws a stone vertically upward with a velocity 16 ms\(^{-1}\). It reaches the water surface in a time of 5 s. In the next 0.2s, the diver can hear the sound from the water surface. The speed of sound is (acceleration due to gravity \( g = 10 \) ms\(^{-2} \))
The sum of the series \( 1 - \frac{2}{3} + \frac{2.4}{3.6} - \frac{2.4.6}{3.6.9} + \cdots \infty \) is:
For \(|x|<\frac{1}{\sqrt{2}}\) the coefficient of \(x\) in the expansion of \(\frac{(1-4x)^2(1-2x^2)^{1/2}}{(4-x)^{3/2}}\) is
The circumference of a circle passing through the point \( (4, 6) \) with two normals represented by \( 2x - 3y + 4 = 0 \) and \( x + y - 3 = 0 \) is:
If \( z = x+iy \), \( x^2+y^2 = 1 \) and \( z_1 = e^{i\theta} \), then the expression \( \frac{z_1^{2n-1} - 1}{z_1^{2^n-1} + 1} \) simplifies to:
Let \( A, B, C, D, \) and \( E \) be \( n \times n \) matrices, each with non-zero determinant. If \( ABCDE = I \), then \( C^{-1} \) is:
If \(2.4^{2n+1} + 3^{3n+1}\) is divisible by \(k\) for all \(n \in \mathbb{N}\), then \(k\) is:
A boy throws a ball with a velocity \(V_0\) at an angle \(\alpha\) to the ground. At the same time, he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of:
The square root of \( 7 + 24i \) is:
What is the overall order of the reaction which has the following rate expression? Rate = k[A]$^\frac{1}{2}$[B]$^\frac{3}{2}$
Which of the following statements are incorrect with respect to nucleotides?
(A) Purines and pyrimidines are nitrogenous bases.
(B) Nucleotides are non-enzymatic molecules.
(C) Phosphate group is linked to – OH of 5′ C of a nucleoside through phosphoester linkage.
(D) In RNA, every nucleotide residue has an additional – OH group present at 2′ position in the ribose.
(E) Thymine is an example of Pyrimidine.
Choose the correct answer from the options given below:
Re-arrange the following parts of a sentence in their correct sequence to form a meaningful sentence:
(A) for organizations which provide
(B) services to customers on a face-to-face basis,
(C) employees with whom they deal is very important
(D) the quality of the relationship between customers and
Choose the correct answer from the options given below :
Choose the word closest in meaning to the underlined word:
Why did you make that flippant remark about her choice of clothes?
\( x \) g of an organic compound was analysed by Kjeldahl’s method for the estimation of nitrogen. The ammonia gas evolved from the compound was passed into 100 mL of 0.2 M H\(_2\)SO\(_4\). The excess of acid required 40 mL of 0.5 M NaOH solution for complete neutralisation. What is \( x \) when the percentage of nitrogen in it is 46%?
If twice the numerator of a fraction is decreased by 50% and thrice the denominator is increased by 200%, the resultant fraction is \( \frac{121}{150} \). What was the original fraction ?
Match List-I with List-II:
Fibrous Proteins