$\operatorname{cosec}\left(-1110^{\circ}\right)=?$
- A-2
- B$\frac{-2}{\sqrt{3}}$
- C2
- D$\frac{2}{\sqrt{3}}$
Question types
Model Paper 6 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 6 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The minimum value of sin x + cos x is
- A$-2 \sqrt{2}$
- B$\sqrt{2}$
- C$0$
- D$-\sqrt{2}$
Two dice each numbered from 1 to 6 are thrown together. Let A and B be two events given by
A: even number on the first die
B: number on the second die is greater than 4
What is the value of $P ( A \cup B )$ ?
A: even number on the first die
B: number on the second die is greater than 4
What is the value of $P ( A \cup B )$ ?
- A$\frac{1}{4}$
- B$\frac{1}{2}$
- C$\frac{1}{6}$
- D$\frac{2}{3}$
If $\cot \theta=\frac{1}{2}$ and $\sec \phi=\frac{-5}{3}$, where $\theta$ lies in quadrant III and $\phi$ lies in quadrant II, then $\tan (\theta+\phi)=$ ?
- A$\frac{-6}{11}$
- B$\frac{5}{11}$
- C$\frac{2}{11}$
- D$\frac{10}{11}$
In how many ways can the letters of the word 'APPLE' be arranged?
- A90
- B6
- C120
- D60
Find the domain of the relation, $R=\{(x, y): x, y \in z, y=4\}$
View full solution →The intercept cuts-off by a line from y-axis is twice than that from x-axis and the line passes through the point (1, 2). Find the equation of the line.
Write E = (14, 21, 28, 35, 42, ..., 98) in set-builder form.
Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas $y^2-4 y+4 x=0$
View full solution →Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in the following cases:
Vertices at $( \pm 5,0)$, Foci at $( \pm 7,0)$.
View full solution →Given that $, P (5,4,-2), Q (7,6,-4)$ and $R (11,10,-8)$ are collinear points. Find the ratio in which Q divides PR.
View full solution →Let $A=\{1,2,3,4\}, B=\{1,4,9,16,25\}$ and $R$ be a relation defined from $A$ to $B$ as, $R=\{(x, y): x \in A, y \in B$ and $\left.y=x^2\right\}$
i. Depict this relation using arrow diagram.
ii. Find domain of R.
iii. Find range of R.
iv. Write co-domain of R.
View full solution →i. Depict this relation using arrow diagram.
ii. Find domain of R.
iii. Find range of R.
iv. Write co-domain of R.
Using binomial theorem, expand: $(\sqrt[3]{x}-\sqrt[3]{y})^6$
View full solution →Solve the following system of linear inequations:
$\begin{array}{l}3 x-6 \geq 0 \\ 4 x-10 \leq 6\end{array}$
View full solution →$\begin{array}{l}3 x-6 \geq 0 \\ 4 x-10 \leq 6\end{array}$
Let $A=\{a, e, i, o, u\}, B=\{a, d, e, o, v)$ and $C=\{e, o, t, m]$. Using Venn diagrams, verify that: $A \cup(B \cap C)=$ $(A \cup B) \cap(A \cup C)$
View full solution →Find four numbers in GP, whose sum is 85 and product is 4096.
20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the card drawn is,
i. A prime number
ii. An odd number
iii. A multiple of 5
iv. Not divisible by 3.
i. A prime number
ii. An odd number
iii. A multiple of 5
iv. Not divisible by 3.
If $\alpha, \beta$ are two different values of x lying between 0 and $2 \pi$ which satisfy the equation $6 \cos x +8 \sin x =9$, find the value of $\sin (\alpha+\beta)$
View full solution →Differentiate log sin x from first principles.
Prove that $\cos \frac{2 \pi}{15} \cdot \cos \frac{4 \pi}{15} \cdot \cos \frac{8 \pi}{15} \cdot \cos \frac{16 \pi}{15}=\frac{1}{16}$
View full solution →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.
Assertion (A): The proper measure of dispersion about the mean of a set of observations i.e. standard deviation is expressed as positive square root of the variance.
Reason (R): The units of individual observations $x _{ i }$ and the unit of their mean are different that of variance.
Reason (R): The units of individual observations $x _{ i }$ and the unit of their mean are different that of 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.
Arun is running in a racecourse note that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m.
i. Path traced by Arun represents which type of curve. Find the length of major axis? (1)
ii. Find the equation of the curve traced by Arun? (1)
iii. Find the eccentricity of path traced by Arun? (2)
OR
iv. Find the length of latus rectum for the path traced by Arun. (2)
i. Path traced by Arun represents which type of curve. Find the length of major axis? (1)
ii. Find the equation of the curve traced by Arun? (1)
iii. Find the eccentricity of path traced by Arun? (2)
OR
iv. Find the length of latus rectum for the path traced by Arun. (2)
A teacher conducted a surprise test of Mathematics, Physics and Chemistry for class XI on Monday. The mean and standard deviation of marks obtained by 50 students of the class in three subjects are given below:
i. Which of the three subjects shows the highest variability? (1)
ii. What is the coefficient of variation of marks obtained by the students in Chemistry? (1)
iii. What is the coefficient of variation of marks obtained by the students in Physics? (2)
OR
What is the coefficient of variation of marks obtained by the students in Mathematics? (2)
| Subject | Mathematics | Physics | Chemistry |
| Mean | 42 | 32 | 40.9 |
| Standard deviation | 12 | 15 | 20 |
i. Which of the three subjects shows the highest variability? (1)
ii. What is the coefficient of variation of marks obtained by the students in Chemistry? (1)
iii. What is the coefficient of variation of marks obtained by the students in Physics? (2)
OR
What is the coefficient of variation of marks obtained by the students in Mathematics? (2)
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