If $\alpha$ and $\beta$ are acute angles satisfying $\cos 2 \alpha=\frac{3 \cos 2 \beta-1}{3-\cos 2 \beta}$, then $\alpha$ is
- A$\sqrt{2} \cot \beta$
- B$\sqrt{2} \tan \beta$
- C$\frac{1}{\sqrt{2}} \cot \beta$
- D$\frac{1}{\sqrt{2}} \tan \beta$
Question types
Model Paper 3 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 3 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $S$ be the sum, $P$ the product and $R$ be the sum of the reciprocals of $n$ terms of a GP, then $P^2$ is equal to
- A$\left(\frac{R}{S}\right)^n$
- B$\frac{S}{R}$
- C$\frac{R}{S}$
- D$\left(\frac{S}{R}\right)^n$
If $A \subset B$, then
- A$A^e \subset B^e$
- B$B^e \not \subset A^c$
- C$A^c=B^c$
- D$B^e \subset A^c$
A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for the shortest board if the third piece is to be at least 5 cm longer than the second?
- A$3 \leq x \leq 91$
- B$3 \leq x \leq 5$
- C$5 \leq x \leq 91$
- D$8 \leq x \leq 22$
The coordinates of the foot of perpendiculars from the point $(2,3)$ on the line $y=3 x+4$ is given by
- A$\frac{2}{3},-\frac{1}{3}$
- B$\frac{10}{37},-10$
- C$\frac{37}{10}, \frac{-1}{10}$
- D$\frac{-1}{10}, \frac{37}{10}$
Find the of derivative of the function from the first principle: $\sin x^2$.
View full solution →If $A=\{1,2,3), B=\{3,4\}$ and $C=\{4,5,6\}$, find
i. $A \times(B \cap C)$
ii. $(A \times B) \cap(A \times C)$
View full solution →i. $A \times(B \cap C)$
ii. $(A \times B) \cap(A \times C)$
Find the equation of the perpendicular bisector of the line joining the points (1, 3) and (3, 1).
Find the equation of the circle which touches the lines $4 x-3 y+10=0$ and $4 x-3 y-30=0$ and whose centre lies on the line $2 x + y =0$.
View full solution →Solve inequation and represent the solution set on the number line: $\frac{2 x-1}{12}-\frac{x-1}{3}<\frac{3 x+1}{4}$ where $x \in R$
View full solution →Draw the graph of the Greatest Integer Function.
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 →Let $A=\{a, e, i, o, u\}, B=\{a, d, e, o, v)$ and $C=\{e, o, t, m]$. Using Venn diagrams, verify that: $A \cap(B \cup C)=$ $(A \cap B) \cup(A \cap C)$
View full solution →If $( a + ib )=\frac{c+i}{c-i}$, where c is real, prove that $a ^2+ b ^2=1$ and $\frac{b}{a}=\frac{2 c}{c^2-1}$.
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.
Prove that: $\tan 20^{\circ} \tan 30^{\circ} \tan 40^{\circ} \tan 80^{\circ}=1$
View full solution →If $\cos x=-\frac{3}{5}$ and $x$ lies in the IIIrd quadrant, find the values of $\cos \frac{x}{2}, \sin \frac{x}{2}$ and $\sin 2 x$.
View full solution →Find the three numbers in GP, whose sum is 52 and sum of whose product in pairs is 624.
Find the derivative of x sinx from first principle.
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.
Ashish is writing examination. He is reading question paper during reading time. He reads instructions carefully. While reading instructions, he observed that the question paper consists of 15 questions divided in to two parts part I containing 8 questions and part II containing 7 questions.
i. If Ashish is required to attempt 8 questions in all selecting at least 3 from each part, then in how many ways can he select these questions (1)
ii. If Ashish is required to attempt 8 questions in all selecting 3 from I part, then in how many ways can he select these questions (1)
iii. If Ashish is required to attempt 8 questions in all selecting 4 from part I and 4 from part II, then in how many ways can he select these questions (2)
OR
If Ashish is required to attempt 8 questions in all selecting 6 from one section and remaining from another section, then in how many ways can he select these questions (2)
i. If Ashish is required to attempt 8 questions in all selecting at least 3 from each part, then in how many ways can he select these questions (1)
ii. If Ashish is required to attempt 8 questions in all selecting 3 from I part, then in how many ways can he select these questions (1)
iii. If Ashish is required to attempt 8 questions in all selecting 4 from part I and 4 from part II, then in how many ways can he select these questions (2)
OR
If Ashish is required to attempt 8 questions in all selecting 6 from one section and remaining from another section, then in how many ways can he select these questions (2)
For a group of 200 candidates, the mean and the standard deviation of scores were found to be 40 and 15 , respectively. Later on it was discovered that the scores of 43 and 35 were misread as 34 and 53, respectively.
i. Find the correct variance. (1)
ii. What is the formula of variance. (1)
iii. Find the correct mean. (2)
OR
Find the sum of correct scores. (2)
| Student | English | Hindi | S.st | Science | Maths |
| Ramu | 39 | 59 | 84 | 80 | 41 |
| Rajitha | 79 | 92 | 68 | 38 | 75 |
| Komala | 41 | 60 | 38 | 71 | 82 |
| Patil | 77 | 77 | 87 | 75 | 42 |
| Pursi | 72 | 65 | 69 | 83 | 67 |
| Gayathri | 46 | 96 | 53 | 71 | 39 |
ii. What is the formula of variance. (1)
iii. Find the correct mean. (2)
OR
Find the sum of correct scores. (2)
Generate a Model Paper 3 paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.