If $\cos A = m \cos B$, then $\cot \frac{A+B}{2} \cot \frac{B-A}{2}=$
- A$\frac{m-1}{m+1}$
- B$\frac{m-2}{m+2}$
- C$\frac{m+2}{m-2}$
- D$\frac{m+1}{m-1}$
Question types
Model Paper 9 question types
45 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
45
Questions
6
Question groups
5
Question types
01
M.C.Q (1 Marks)
18 Q→022 Marks Questions
7 Q→033 Marks Question
9 Q→045 Marks Questions
6 Q→05Assertion (A) & Reason (B) MCQ
2 Q→06Case study (4 Marks)
3 Q→Sample Questions
Model Paper 9 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In how many ways can a committee of 5 members be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?
- A50
- B200
- C25
- D100
Mark the Correct alternative in the following: $8 \sin \frac{x}{8} \cos \frac{x}{2} \cos \frac{x}{4} \cos \frac{x}{8}$ is equal to
- Asin x
- B8 cos x
- Ccos x
- D8 sin x
If $A$ and $B$ are two given sets, then $A \cap(A \cap B)^C$ is equal to
- AB
- BA
- C$A \cap B ^{ C }$
- D$\phi$
The solution set of 6x - 1 > 5 is :
- A$\{x: x>1, x \in N\}$
- B$\{x: x>1, x \in R\}$
- C$\{x: x<1, x \in N\}$
- D$\{x: x<1, x \in W\}$
if O is the origin and Q is a variable point on y2 = x. Find the locus of the mid-point of OQ.
Write down all possible subsets of A = (1, {2, 3}).
Find the equations to the circles which pass through the origin and cut off equal chords of length 'a' from the straight lines y = x and y = -x.
Find equation of circle whose end points of its diameter are (-2, 3) and (0, -1).
Evaluate $\lim _{x \rightarrow 0} \frac{e^{k x}-1}{x}$.
View full solution →Let $f=\left\{\left(x, \frac{x^2}{1+x^2}\right): x \in R\right\}$ be a function from R into R . Determine the range of f .
View full solution →If $u=\{1,2,3,4,5,6,7,8,9,10,12,24\}$
$A=\{x: x$ is prime and $x \leq 10\}$
$B=\{x: x$ is a factor of 24$\}$
Verify the following result
i. $A - B = A \cap B^{\prime}$
ii. $(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$
iii. $(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$
View full solution →$A=\{x: x$ is prime and $x \leq 10\}$
$B=\{x: x$ is a factor of 24$\}$
Verify the following result
i. $A - B = A \cap B^{\prime}$
ii. $(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$
iii. $(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$
Evaluate $\left[\frac{1}{1-4 i}-\frac{2}{1+i}\right]\left[\frac{3-4 i}{5+i}\right]$ to the standard form.
View full solution →Express $(1-2 i)^{-3}$ in the form of $(a+i b)$.
View full solution →Find the expansion of $\left(3 x^2-2 a x+3 a^2\right)^3$ using binomial theorem.
View full solution →A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that:
i. one is red and two are white
ii. two are blue and one is red
iii. one is red.
i. one is red and two are white
ii. two are blue and one is red
iii. one is red.
Find the sum of the following series up to n terms:
i. 5 + 55 + 555 + ……
ii. 6 + .66 + .666 + …..
i. 5 + 55 + 555 + ……
ii. 6 + .66 + .666 + …..
Prove the following identity: $\cos ^3 2 x+3 \cos 2 x=4\left(\cos ^6 x-\sin ^6 x\right)$.
View full solution →Differentiate $\frac{\cos x}{x}$ from first principle.
View full solution →Prove that: $\tan 20^{\circ} \tan 30^{\circ} \tan 40^{\circ} \tan 80^{\circ}=1$
View full solution →Assertion (A): If each of the observations $x _1, x _2, \ldots, x _{ n }$ is increased by a, where a is a negative or positive number, then the variance remains unchanged.
Reason (R): Adding or subtracting a positive or negative number to (or from) each observation of a group does not affect the variance.
Reason (R): Adding or subtracting a positive or negative number to (or from) each observation of a group does not affect the variance.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Assertion (A): The expansion of $(1+ x )^{ n }=n_{c_0}+n_{c_1} x+n_{c_2} x^2 \ldots+n_{c_n} x^n$.
Reason (R): If $x=-1$, then the above expansion is zero.
Reason (R): If $x=-1$, then the above expansion is zero.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Consider the data
i. Find the standard deviation. (1)
ii. Find the variance. (1)
iii. Find the mean. (2)
OR
Write the formula of variance? (2)
View full solution →| $x_i$ | 4 | 8 | 11 | 17 | 20 | 24 | 32 |
| $f _{ i }$ | 3 | 5 | 9 | 5 | 4 | 3 | 1 |
ii. Find the variance. (1)
iii. Find the mean. (2)
OR
Write the formula of variance? (2)
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