List of practice Questions

The graph between two temperature scales $P$ and $Q$ is shown in the figure Between upper fixed point and lower fixed point there are 150 equal divisions of scale $P$ and 100 divisions on scale $Q$ : The relationship for conversion between the two scales is given by:-

For a moving coil galvanometer, the deflection in the coil is $005$ rad when a current of $10 \,mA$ is field is $0,01 \,T$ and the number of turns in the coil is $200$ , the area of each tum (in $cm ^2$ ) is :

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are:- 
A. Real 
B. Erect 
C. Smaller in size then object 
D. Laterally inverted 
Choose the most appropriate answer from the options given below:

The equivalent resistance between A and B is _________.

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is:-

If the equation of the plane passing through the point $(1,1,2)$ and perpendicular to the line $x-3 y+$ $2 z-1=0=4 x-y+z$ is $A t+ B y+ C z=1$, then $140( C - B + A )$ is equal to______

If for log_{cos x} (cot x) - 4log_{(sin x)} cot x = 1, x = sin^-1 \((\frac{\alpha+\sqrt{\beta}}{2})\). Find (α + β), given x ∈ \((0,\frac{\pi}{2})\)

Match List I with List II

	List I		List II
A.	Young's Modulus (Y)	I.	[M L-1 T-1 ]
B.	Co-efficient of Viscosity (η)	II.	[M L2 T-1 ]
C.	Planck's Constant (h)	III.	[M L-1 T-2 ]
D.	Work Function (ϕ)	IV.	[M L2 T-2 ]

Choose the correct answer from the options given below:

Suppose \( f: \mathbb{R} \to (0, \infty) \) be a differentiable function such that: \( 5f(x + y) = f(x) \cdot f(y), \quad \forall x, y \in \mathbb{R} \). If \( f(3) = 320 \), then the value of:\( \sum_{n=0}^{5} f(n) \) is equal to:

Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1,2 , 3 and 5 , and are divisible by 15 , is equal to _____

Let \( \lambda_1 < \lambda_2 \) be two values of \( \lambda \) such that the angle between the planes:
\( P_1 : \vec{r} \cdot (3\hat{i} - 5\hat{j} + \hat{k}) = 7 \) 
\( P_2 : \vec{r} \cdot (\lambda\hat{i} + \hat{j} - 3\hat{k}) = 9 \)
is \( \sin^{-1}\left(\frac{2\sqrt{6}}{5}\right) \). Then, the square of the length of the perpendicular from the point \( (38\lambda, 10\lambda, 2) \) to the plane \( P_1 \) is:

Let \( A = \begin{pmatrix} m & n \\ p & q \end{pmatrix} \), \( d = |A| \neq 0 \), and \( |A - d(\text{Adj}(A))| = 0 \). Then

Let \( z = 1 + i \) and \( z_1 = \frac{1 + \bar{z}}{z(1 - z) + 1} \), where \( \bar{z} \) denotes the conjugate of \( z \). Then\(\frac{12}{\pi} \arg(z_1)\) is equal to:

The $4^{\text {th }}$ term of $G P$ is $500$ and its common ratio is $\frac{1}{m}, m \in N$ Let $S_n$ denote the sum of the first $n$ terms of this GP If $S_6>S_5+1$ and $S_7< S_6+\frac{1}{2}$, then the number of possible values of $m$ is

\( \lim_{x \to 0} \frac{48 x^4}{x} \int_0^x \frac{t^3}{t^6 + 1} \, dt \) is equal to:

The value of $\frac{8}{\pi} \int\limits_0^{\frac{\pi}{2}} \frac{(\cos x)^{2023}}{(\sin x)^{2023}+(\cos x)^{2023}} d x$ is

Let a tangent to the curve $9 x^2+16 y^2=144$ intersect the coordinate axes at the points $A$ and $B$. Then, the minimum length of the line segment $AB$ is

A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses If he can choose at most two language courses, then the number of ways he can choose five courses is

The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is

Let $C$ be the largest circle centred at $(2,0)$ and inscribed in the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$If $(1, a)$ lies on $C$, then $10 \alpha^2$ is equal to

Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial number. For example, the number 77777 has serial number 1. Then the serial number of 35337 is _________

Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event .
Given below are two statements : 
(S1): If $P ( A )=0$, then $A =\emptyset$ 
(S2): If $P(A)=1$, then $A=\Omega$
Then

Let the coefficients of three consecutive terms in the binomial expansion of (1 + 2x)n be the ratio 2 : 5 : 8. Then the coefficient of the term, which is in the middle of these three terms, is _______.

The equation $x^2-4 x+[x]+3=x[x]$, where $[x]$ denotes the greatest integer function, has :