BITSAT Practice Test 51 for JEE & BITSAT Exams

Question 1

For what values of x are the rate of increase of function y = x³ - 5x² + 5x + 8 is twice the rate of increase of x?

Question 2

What value of c satisfy the mean value theorem for f(x) = 3x² + 5x – 2 in interval [-1,1]?

Question 3

Find the direction cosines of a straight line whose projections of the coordinate axis OX, OY and OZ are 5, 12, and 13 respectively.

Question 4

If the lines

and

are coplanar. Find the value of

Question 5

Find the value of

if

Question 6

In the following question, a sentence is given with a blank to be filled in with an appropriate word. Select the correct alternative out of the four and indicate it by selecting the appropriate option.

While the newly elected president’s speech seems original, it contains a/an ______ to a speech made by another world leader.

Question 7

A and B together do a job in 15 days and A alone could do the same job in 20 days. How many days would B take to do half the job if he worked alone?

Question 8

A nucleus has a half life of 34.2 years. It is decaying into another nucleus. How long it will take to change 90℅ of it to another nucleus?

Question 9

In a sample there are 15% undecayed radioactive nuclei present at any instant of time. After 20 minutes later, the number of undecayed nuclei reduces to 7.5%. Calculate the mean life of nuclei.

Question 10

A metal has 36 neutrons and a beam of X-rays is targeted on it. The ratio of atomic radius of the target atom and ₂He⁴ is 14^1/3. What is the atomic number?

Question 11

A thin convex lens of focal length ‘f’ is put on a plane mirror as shown in the figure. When an object is kept at a distance ‘a’ from the lens – mirror combination, its image is formed at a distance

in front of the combination. The value of ‘a’ is:

Question 12

5 mL of 8 N HNO₃, 4.8 mL of 5 N HCl and a certain volume of 17 M H₂SO₄ are mixed together and made upto 2 litres 30 mL of this acid mixture exactly neutralizes 42.9 mL of Na₂CO₃. 10H₂O in 100 mL of water. Calculate the amount of sulphate ions in g present in the solution.

Question 13

Which of the following complexes does not easily react?

Question 14

Consider the given reaction

X and Y respectively are:

Question 15

By what factor does the average velocity of a gaseous molecule increase when the absolute temperature is doubled ?