List of practice Questions

Speedometer of a car measures

If $(1 + x + x^2)^{48} = a_0 + a_1x + a_2x^2+ ..... + a_{96}x^{96},$ then value of $a_0-a_2 +a_4 -a_6..... + a_{96} $ is

In a shop, the marked price of an article is Rs.4000. The shopkeeper gives some discount on that article and earns profit of Rs.550. Find the percentage discount on that article,if its cost price is Rs.2250.

The common characteristics between brinjal and wheat can be observed maximum at the level of their.

Select the option(s) in which rate of SN1 is faster in II than I?

Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.

In a given AC circuit consisting of a resistor R and an inductor L and source emf, two voltmeter V₁ & V₂ are connected as shown. If V₂ = 36 volts then inductance of inductor is (Resistance R is √91Ω.)

The two structures written below represent 

Directions: The following question has four choices, out of which one or more are correct. Assume that the nuclear binding energy per nucleon $\left(\frac{B}{A}\right)$ versus mass number (A) is as shown in the figure. Use this plot to choose the correct answer(s) from the choices given below.

Convert the following temperatures to the Celsius scale.
(a) 293 K
(b) 470 K

A plane x + 2y + 2z – 15 = 0 cuts a sphere x² + y² + z² – 2y – 4z – 11 = 0 in a circular section. What is the radius of the cut section?

Directions: The following question has four choices, out of which one or more are correct. The potential energy function of a particle moving in one dimension is $U=k[x-\frac{x^3}{3a^2}],$ where $a$ and $k$ areconstants. Then,

Directions: The following question has four choices, out of which one or more are correct.In a triangle $\mathrm{\Delta }PQR,\cos (P-R)\cos (Q)+\cos (2Q)=0$Which of the following options is/are correct?

$\int e^{x\log a}\cdot e^{x}dx$ is equal to

If the coordinates of one end of a diameter of the circle  x²+y²+4x–8y+5=0, is (2,1), the coordinates of the other end is 

The cubic equation whose roots are the AM, GM and HM of the roots of x² - 2px + q² = 0 is

The number of solutions of the equation tan x + sec x = 2 cos x and cos x ≠ lying in the interval (0, 2π) is

 If ⁿC4, ⁿC5 and ⁿC6 are in A.P., then n is 

The radius of a cylinder is increasing at the rate of 3 m/s and its altitude is decreasing at the rate of 4 m/s. The rate of change of volume, when radius is 4 m and altitude is 6 m, is

If the coefficients of 5th, 6th and 7th terms in the expansion of (1+x)n are in A.P. then n =

The radius of a circle is increasing at the rate of 0.1 cm/s. When the radius of the circle is 5 cm, the rate of change of its area is

The door of a running refrigerator inside a closed room was left open. Which of the following observations will be seen?

The percentage of carbon in acetic acid is

In a triangle ABC, tan C < 0. Then